in-19-25-express-each-answer-in-simplest-radical-form-check-each-answer-the-lengths-of-the-bases-of-

Question

In $19-25,$ express each answer in simplest radical form. Check each answer. 
The lengths of the bases of a trapezoid are $x+10$ and $3 x+2$ and the length of the altitude is 2$x$ . If the area of the trapezoid is $40,$ find the lengths of the bases and of the altitude.

Elizabeth Xu · Accepted Answer

discussion. Here we have a chapas oId with two bases. One base is X plus 10 Toby one sex was 10 and B two is equal to three X plus two with a height or altitude of two max. We also know that the area is equal to 40. So we know that to find the area here we have B one plus B two divided by two times the height and this is equal to area. Where they should be written is high. Since we know each of the values here, you know that be one is you could expose 10 and B two&#x27;s equal to three expose to H is equal to X In the areas of the 40 we consult for X so we have these twos cancel out here in the numerator we have for ex post 12 times X is equal to 40. So for X squared plus 12 x minus 40 is you go to zero dividing everything before we have X squared. Plus three x minus 10 is equal to zero To solve for X, we can use the quadratic formula. You have negative B plus finest the square root O B squared minus four times a times C about a pipe to a. This is equal to negative. Three cost. Minus the square root. So 49 to guarded by two four negative three plus minus seven divided by two So two options are negative. Three plus seven Divided by two, which is equal to two or negative three minus 72 out of my to it is equal to negative five. But because here we&#x27;re solving for X, which and the height is equal to two times X, we have to make sure that next must be positive because we cannot have a negative height. So that means that acts cannot equal of your five so X is equal to two. Therefore, our bases are equal to two plus 10 which is equal to 12. Three times two plus two. Musical to eight, and the height or altitude is equal to two times two, which is equal to four. So be one is you got 12 be to you go to eight and altitude is equal to four

Bahar Tehranipoor · Answer

in this exercise, we have a question that says the length of a rectangle is two feet more than the with, so we can just write that as the length equals two plus the with and the area of the rectangle is two square feet. So we know length times with because that is, our area equals two square feet. We want to find the dimensions of this rectangle, so this is a pretty easy problem. We&#x27;re just given to equations and we want to solve. So what we can do is we can take W or L, and we can replace it in this equation with the this part of the equation in terms of the other. So that&#x27;s a little confusing. But what I mean is we basically just take help and replace it with two plus W so that instead of writing lda vehicles to, we have to pull us over you times w equals two, and that&#x27;s distribute that out. So we have to w plus w squared equals two, and we can actually use the quadratic formula to find our roots of this equation, which will give us our with so to W facilities. Grable&#x27;s to Doesn&#x27;t really look at the form that we warrant, which is a X squared plus B X, Let&#x27;s see. And in this case we have w instead of exes. So let&#x27;s try to get the two on the other side, and then we&#x27;ll have W squared plus two w. We then subtract two. We have minus two equals zero. So this is our equation, and we&#x27;re gonna use the quadratic formula here. So let&#x27;s take opposite Be so we have negative use. Negative, too, plus or minus the square root of B squared minus for a C. So B squared is two squares of four minus four. A is one time See, which is negative, too, over to a and here is one switches over to. Now let&#x27;s clean up what&#x27;s inside the square root four minus four times one has a tutu is just four plus four times one times two so four times one times two is 84 plus a in the squares. Because his people&#x27;s negative to plus or minus the square root of four plus eight, which is sort of 12 over to now, a square of 12 can actually be some fight down because it&#x27;s four times three in the square to forge is too. So this equals negative to plus or minus the, uh, two times the square root of three over to. So now we can divide a two out. So over the next page, negative too, plus or minus two or three over two. That&#x27;s just now negative one plus or minus the square of three. Because all we did it just to buy the tools out by the two in the native to we have negative one get by the 2 to 2 or three we have three. So now we have negative one plus reminds or three, which gives us roots negative one plus for three or a negative one minus for three. So for the width of a rectangle and for it to be real rectangle, we have to have a positive with is the only way we&#x27;re gonna have an area that is riel. So negative one minus two or three is going to be fully negative. So that can&#x27;t be our with. So we&#x27;re with it must be negative. One plus, Ruth three. Now our length is gonna be to more than that. Sore length is going to be negative. One closer, three plus two. So we have negative one plus for three plus to add that together we get a positive one plus for three. So that is our length and with and really quickly, we can just test that out by multiplying them together. Multiply them together we get negative one. So negative One incident was one that we have negative or three plus for three. And then we have plus three fighter that quickly. Yes, So we have negative one minister through pleasure People&#x27;s three. And that does indeed equal the two that we want. So these are our dimensions.

Elizabeth Xu · Answer

So in this question, here we have a rectangle where the length of the rectangle is four centimeters more than the way. So if the with stop you, that means the lamp ears for plus W. We also know that the measure of the diagonal is equal to 10 centimeters song, so we want to find the dimensions of the rectangle. Well, given this what we know here, the because we have a rectangle in a right triangle year, we know that W squared plus four plus W squared. Is he good to 10 square from Pataki in state From now we expand B A W squared plus 16 plus hate W plus W squaring. Does he go to 100? So to W squared plus C W minus 84 is equal to zero. The body will sides by two because W squared plus four w minus 32 or minus 42 you have read here, 42 is equal to zero. Now, to find the zeros of this equation or softer W, we have negativity plus find a screw B squared minus four times. Hey Dempsey, divided by two A, which is equal to negative four plus minus square root of 1 84 over to because he got four plus minus two room 46 over to what is equal to negative two plus minus root 46. So that means that W can either be equal to negative two. Plus Route 46 were negative two minus 3 46 But we know that negative two minus Route 46 will be a negative number. And because W. Stands for the width of a rectangle and erecting will cannot have a negative width, we can disc lewd. This answer and we have W is equal to negative to or negative two, plus Route 46 so don&#x27;t use equal to negative two plus through 46. We know that the lamp here is four plus w. So four plus W is equal to positive two plus Route 46. So we have our with is negative two plus Route 46 our link is positive two plus Route 46

Amy Jiang · Answer

Okay, so we want to find the area of this trap is oy. What we What we can do first is we confined this area of orb rectangle and then this portion here, our triangle here, if you, with your at this out is here, it is the same rectangle that we have to our left. So let&#x27;s start by finding our this rectangle here. Area of that is equal to our length time there with Well, let&#x27;s notice that we have square root of 288. Um, is that the same as the square root of 72? Let&#x27;s get up. Out. So we&#x27;re gonna divide this by half to get this portion here throwing out 288 is this whole entire thing. So it&#x27;s a So we have discovered up to 88. So let&#x27;s divide that by two. So this is two times 144 and this is 12 sward, so this is equal to 12 on the square root of two. And what about 72? Let&#x27;s see. Um, this is a 36 times two and 36 26 squared, so we can write this as the square root or six square root, too. So we see that, um, if we divide the square root of 288 which is 12 square roots of two by two, we get six square root of two. Okay, so I think, or area of or rectangle, let&#x27;s put a of a rectangle that&#x27;s equal to our length. Times are with our length is the square root of 24 times the square root of actually of six square roots to So that&#x27;s six. And in the square root of 24 which is six times four times two. Okay, so six is Let&#x27;s hurt that out six times four attempts to six is three times to for is two times two times two. So that&#x27;s three times to defer to depart to so we can pull out to square, don&#x27;t you before. So that&#x27;s four times six, which is 24 in the square root of three. Okay, so this is the area of our rectangle. No, our area of our trapezoid. It&#x27;s called that shop that&#x27;s going to be equal to the area of our rectangle, plus half the area of or rectangle, which is equal to the area of our triangle. Does that make sense? Half of our rectangle here is equal to this portion here. Okay, so this gives us 24 square root of bring plus ah, half of 24 the square root of three. That&#x27;s equal to 24 square root of three. Plus call the square root of bring, which is equal to a 36 the square root of three for our area of our chapters, Lloyd.

Maninder Singh · Answer

that given the easier it is, this site is 24 decided scared over 72 on decided to 80. Then we have to find that idea. If he&#x27;s a professor, then we know that it is equal to 1/2 some off. Dead land saves some. Their lone star lives when do height that is distant between their little size, but it is equal to one other Parents exerts Carew off 72 to scale up to here and the height, the distance between them is scheduled to run. People. No, we have been told this thing, but this we will do like this one by two. Not scared. Some people can Betterton as 36 times too. Plus scheduled off. 80 years can be written as 36 die in school dying four into steered 24. Which can Britain eat? Times City This is the quarto one but two, but get out of 36 36 36. Scare uber to blood. No, scheduled of 36 86 and scared for is toe the extent to which 12 diverse 12 scared too into no scared though it can be return is too scared to and too scared City No, we have to solve this thing. So this is a call to burn by two. Now these two have lifetime. So we will ask them. It will give us 18 scare Ruto too in tow. Scare route off six Because Rudolph who interested don&#x27;t we will give us Kyoto six. This too can cancel with this too. So reelected 18 Perrotta to mental scare route off six No, this think and Britain is they attained. Scare it off to into Beirut. Off to into a tree. So we again right Skeletal Texas to into the country. No skeletal who went to scale it up to that is to a full time. The 18 is 36. So our final and that is 36 Scare Route three, you know, scared, Which is that media off the given to preserve

Elizabeth Xu · Answer

this question. Here we have two numbers. Let&#x27;s call it be a action. Why we can say that? Why is a larger of the two numbers? So we know that the larger of the two numbers why is equal to five more than twice the smaller one. So that&#x27;s five plus two X. And we know that small square of a smaller number X were is equal to the larger number. So by and we want to find the two numbers Well, if we know that both of these five close to X and X squared are both equal to why we&#x27;re gonna quite them to each other. So we know that five plus two X is equal to X squared. Then If we subtract two x plus five from both sides of the equation, we got our quadratic equation. X squared minus two X minus five is equal to zero. Now you can use our quadratic formula to solve for what X is equal to so yeah to, or a negative P plus finest square room, a P square minus four a c divided by two way. This is equal to two plus finest square root of 24 over to which is equal to two post minus two Route six over to or one of plus minus root. Six. So that means that actually either equal to one plus Route six or X is equal to one minus route. Six. Well, if X is equal to one plus Route six, we know that why is able to five plus two X? That means that why is equal to five plus two times X, which is to plus 26 or seven plus two. Route six now in excess, equal to one minus root sex wise equal to five plus two minus two. Route six Or why is equal to seven minus two. Route six So you have to situations here when ecstasy goto one plus fruit. Six. Why is he going to seven plus two? Route six and when X is equal to one minus Route six. Why is equal to seven minus two Route six

Problem

The altitude, $\overline{C D}$ , to the hypotenus…

Problem 23 Hard Difficulty

In $19-25,$ express each answer in simplest radical form. Check each answer.
The lengths of the bases of a trapezoid are $x+10$ and $3 x+2$ and the length of the altitude is 2$x$ . If the area of the trapezoid is $40,$ find the lengths of the bases and of the altitude.

Answer

Bases: 12 and 8
Altitude: 20

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Ann Xavier Gantert

Algebra 2 and Trigonometry

Anna Marie V.

Alayna H.

Maria G.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

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Bases: 12 and 8Altitude: 20

Algebra 2 and Trigonometry

Anna Marie V.

Alayna H.

Maria G.

Michael J.

Absolute Value - Example 1

Absolute Value - Example 2

Ann Xavier GantertAlgebra 2 and Trigonometry

Anna Marie V.

Alayna H.

Maria G.

Michael J.

Bases: 12 and 8
Altitude: 20

Ann Xavier Gantert

Algebra 2 and Trigonometry