the-area-of-a-rectangle-is-25sqrt35-square-feet-and-the-width-is-10sqrt5-feet-find-the-length-of-the

Question

The area of a rectangle is 25$\sqrt{35}$ square feet and the width is 10$\sqrt{5}$ feet. Find the length of
the rectangle in simplest radical form.

M S · Accepted Answer

So we&#x27;re given that the era rectangle is 25 35. So I know that area is 25 times very 30 were also given that the wit is time to square it is, But they were looking for the link I never went in simples for we know that area is Link Tom&#x27;s wit. What if you saw for Blake Foreign divide both sides by the wit So Lee is area divided by with so the situation will calm them standing so like this area divided by wood. So I&#x27;m gonna substitute in area is 25 Route 35 and with this tin route, but so automatically we can reduce our regular numbers about dividing by the greatest moment factor. So to go someone factor between 10 and 25. Spot 25 divided by five gets a spot and 10 divided by five gets us to So we have five work too. And then when you combine these radicals because they have the same right, so just radical square it of 35 over five and I&#x27;m gonna do the same thing. I wanted to buy the top bottom by the great become a factor in this case, it&#x27;s Father 35 divided by five years. A seven and five divided by five gives us boy. So we have five over two times the square root of seven. And that&#x27;s as far as we can. Simplify this expression and be sure to include units. In this case, it&#x27;s Bates. It is just like so it&#x27;s not beat, squared or cute or anything. It&#x27;s just

Finian Lickona · Answer

So we are given that the dimensions of a rectangle are 15 feet by 10 feet and we want to find the length of the diagonal and simplest radical form. Now the length of diagonal is really just going to be the hypothesis of the right try and go forward by these two sides of the rectangle. If we recall, we confined the length of that hype oddness using the Pythagorean there. So 15 squared is 225 110 squared is 100 that&#x27;s equal to the high Patna squared. If we just want the high partners, we have to take the square root of both quantities. So we have the hype. Oddness is equal to the square root of 325 now. This isn&#x27;t quite the simplest radical form, because we can actually rewrite 325 as 13 times 25 25 is a perfect square, so we can factor that out of the radical as of five. So our hypothesis length is actually going to be five radical 13

Sarah Wharton · Answer

in this problem, we need to find the area of a rectangle where one side is equal to 12 route to and the other side is equal to route 50. To do this, we need to know that the area of a rectangle is equal to the base times the height. So when I write this out, I have a for area is equal to 12 route to times the square root of 50. This could be simplified by combining the two and 50 in the same radical sign says will be equal to 12 times the square root of two times 50 two times 50 is 100 leaving us with 12 times a square root of 100. The square root of 100 is 10. So we have 12 times 10 which leaves us with 120. But we have to have our units. So I&#x27;m gonna write our full answer as the area is equal to 120 was measured in feet, feet squared. And that&#x27;s our final answer

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.

Ashley Volpe · Answer

All right. So what we know in this problem? What they tell us in this problem is that we have a rectangle and that we know the area of that rectangle is 24 square inches. They give us the length of the rectangle as being the square root of five plus one, and they want us to find the with. So we think back to our geometry. And the area of a trying area of a rectangle is length Tom&#x27;s with. So I&#x27;ve got a link. I&#x27;ve got an area I need a with. Well, that&#x27;s a reverse that multiplication. That&#x27;s a division question. My with is equal to my area, divided by my length. So in this case, that&#x27;s gonna be 24 divided by radical five plus one. Now, that&#x27;s not rationalised. I can&#x27;t leave that radical in that denominator, so I&#x27;m gonna have to rationalize. So I got the square root of five minus one top and bottom, and then I need to do a little distribution or boiling whatever the case may be to get this question. So here, we&#x27;re gonna distribute. So we get 24 radical five minus 24 on the denominator side radical. Five times radical. Five is five. And then you&#x27;ve got a positive radical five and a negative. Those they&#x27;re gonna cancel. So then plus one and negative one makes minus one. Continuing to clean that up. Five minus one is four. Now, if you look at that, you&#x27;ll notice you got a 24 24 a four. Well, let&#x27;s divide those All that for that&#x27;s going to give me 66 and one. So the answer I&#x27;m gonna end up with here is six radical five minus six since we&#x27;re dealing in inches and this was a with we&#x27;re gonna have six radical five minus six inches as our final answer.

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

Problem

The area of a right triangle is 6$\sqrt{2}$ squar…

Problem 30 Medium Difficulty

The area of a rectangle is 25$\sqrt{35}$ square feet and the width is 10$\sqrt{5}$ feet. Find the length of
the rectangle in simplest radical form.

Answer

$\frac{5}{2} \sqrt{7} f t$

Related Courses

Algebra 2 and Trigonometry

Related Topics

Discussion

Top Educators

Recommended Videos

Watch More Solved Questions in Chapter 3

Video Transcript

Ann Xavier Gantert

Algebra 2 and Trigonometry

What do you need help with?

Textbooks

Ask a question

Courses

AI Tutor

$\frac{5}{2} \sqrt{7} f t$

Algebra 2 and Trigonometry

Ann Xavier GantertAlgebra 2 and Trigonometry

Ann Xavier Gantert

Algebra 2 and Trigonometry