the-ratio-of-the-length-to-the-width-of-a-rectangle-is-7-3-the-area-of-the-rectangle-is-336-square-c

Name: the ratio of the length to the width of a rectangle is 7 3 the area of the rectangle is 336 square c
Uploaded: 2020-05-20
Duration: 2 min 5 s
Channel: Numerade
Description: The ratio of the length to the width of a rectangle is 7 : 3. The area of the rectangle is 336 square centimeters. What are the dimensions of the rectangle?

Question

The ratio of the length to the width of a rectangle is 7 : 3. The area of the rectangle is 336 square centimeters. What are the dimensions of the rectangle?

Julie Silva · Accepted Answer

So in this problem, what we&#x27;re told is that the ratio of the length to the width of a rectangle is 7 to 3. As I mentioned here, now we&#x27;re told that the area of a rectangle is 336 centimeter squared. We want to find the dimensions, meaning we want to find the length and the width will remember to find the area of a rectangle, we simply multiply the length times toe with Well, because we know the ratio is in from the length to the with 723 And we don&#x27;t know that scale factor that we would multiply both terms by what we&#x27;re going to do is call that X. So we&#x27;re gonna write rewrite our ratio in the form of seven X to three X. So now we&#x27;re gonna substitute seven X and for El and three X and for W. And then we&#x27;re gonna solve for X. Now, remember, we know the areas 336 so we have 336 is equal to seven x times three x Well, seven Next times three X is 21 x squared. So we&#x27;re gonna have 300. Oops, sorry, that should have said 36. There do you have 336 is equal to 21 X where and now we just have to solve this equation for X first, we&#x27;re gonna divide both sides by 21 336. Divided by 21 is 16. So we have 16 is equal to x word. So we find take the square root of both sides. Typically, we will put our possum minus side so we would find X is equal to while the square the 16 is four you have plus or minus four. But think about what X represents. It&#x27;s our scale faster and our length and width can&#x27;t be negative. So in this case, acts is just equal to four. So to find our dimensions were simply going to substitute acts in for our ratio. Seven x to three x. Therefore, the length will be seven times for which is 28 our units here centimeters and there with can be found by multiplying three times, for which is 12. So we&#x27;ll have 12 centimeters, so our dimensions are 28 centime

Amy Jiang · Answer

Okay, so we&#x27;re given that the length of a rectangle is to more than three times with the length is it was a two plus three times that with on the perimeter is equal to 28 inches were asked to find the dimensions of a rectangle. So recall what perimeter is. It&#x27;s adding up all of our science. So if this year is that with and this is our like or length is two plus three w And if you have a rectangle, are opposite sides of the same. So this is two plus three w. And this is a w. Okay, so perimeter that secret to 28th and recall that this is equal to two times are at length, plus two times are with. Well, let&#x27;s plug in our formula for our link. We should. This is to cluster and then two plus two the week Now we can solve for W here we want to solve for R Length and Irwin. Okay, so let&#x27;s multiply out that too. I know. Let&#x27;s combine my terms. So that&#x27;s four plus it of you. And now I want to subtract both sides by four to get rid of this four next to our variable. So we got 24 is equal to eight of you. And what&#x27;s 24 divided by AIDS. Will we get that are with is equal to three. So it&#x27;s right that back up there. Okay, so we found her with and recall that are length is dependent on our with that&#x27;s our length is equal to two, but three times are just three to get to plus nine, and that&#x27;s equal to love it, and this isn&#x27;t inches.

Georgiann Andersen · Answer

we&#x27;re gonna find the dimensions of the rep Tango one. You know that the ratio of the linked to the witness by 24 and the perimeter is 72. This this problem number 20. So we know that length over with it&#x27;s gonna equal to five over four and the perimeter equals 72 inches. So that means that the perimeter is gonna be too times five X plus two times or ex equal 72. So what we&#x27;re gonna do is we&#x27;re gonna find out what the exits here, 10 X plus eight x it&#x27;s gonna be 72. 18 axe equal 72 devivo 18. Our ex is gonna be four. So now we can take that and we can substitute that back yet. So if we know that the length it&#x27;s five acts we&#x27;re gonna take and substitute foreign soar like it&#x27;s gonna be 20 inches are with we said was for X so we can take them. Excuse me the four times before, we&#x27;re gonna get 16 inches. So that is our dimensions

Meredith Moody · Answer

in order to find the dimensions of my rectangle, I have Teoh used the area formula of length times width Teoh solve for my wits and then use that value to solve for my length. So I don&#x27;t know what with is, but I do know that the length is twice the width minus seven. And so when I set up this equation over here on the right, I have this to w minus seven. That quantity actually stands for my late. So I have leave times with people&#x27;s 30. So I&#x27;m gonna do the distributive property here and come up with a quadratic equation. So if I do w times to w I get to W Square and then w times a negative seven is negatives that until you equals 30. Now I&#x27;m gonna put this in standard form some of the subtract 30 from both sides and I get to W Square minus seven. W, minus 30 equals zero. Now I&#x27;m gonna factor this, and I know that since my C term is negative, I&#x27;m going to have one addition on one subtraction factor. And since two is prime my coefficient of my variable, I know that I&#x27;m gonna have to w and then w in my factors. So now I have to work with my factors of 30 to figure out. Ah, what the combination is that&#x27;s going to give me negative seven w So I&#x27;m gonna factor 30. Now I get to times 15 in three times five. So I get two times, three times five. And I have to be careful because whatever combination I use, one of them&#x27;s gonna be multiplied by two. So, uh, if I do, let&#x27;s say I do two times three, which is six. So then if I say okay, let&#x27;s have, um the let&#x27;s do six and five. Well, six times two is 12. That would be doubles and then 12 and five. The difference there it&#x27;s seven. So that works. Whereas if I had done the other way, like two times five, that would been 10 and 10 and six only gives me a difference before, so I&#x27;m gonna use six and five, because that&#x27;s gonna give me six times five is 30 and two times six, which again comes from this coefficient. A minus five. That should be a minus five is gonna give me seven. That means that the difference is gonna be negative. So my larger number is gonna have to be negative. So this 12 is actually gonna have to be negative. So the six is gonna go there when the fire was gonna go here. So this really is gonna be negative. 12 plus five is gonna give me negative seven. So now I have my factors in its southern equal to zero in order to solve. So I get minus five and that gives me to w equals negative five. I&#x27;m gonna divide both sides by two. And I get w equals negative Five halves. Well, that is not right, because you can&#x27;t have a whips the negative. So I&#x27;m going to check my stuck it. One, which is w minus minus six equals zero. Have six to both sides. So I get that. My wit is six now, because my Witte IHS six on a substitute that in here and say two times six minus seven. Well, it&#x27;s your time. Six is 12 in 12 minutes. Seven is five. So my wick is six on my legs is five. And if I dio six times five, that is, in fact, 30. So my solution is that my lace, his five and my witness six

Kayleah Tsai · Answer

he was told that the perimeter of a rectangle is 294 centimeters, and we&#x27;re also told that the with is 57 centimeters and we&#x27;re looking for the length. So first we know that the perimeter is equal to two times that with plus two times the life. And this is for ah rectangle because it&#x27;s too with sides and two lengths sides. So now we can simply just plug in the perimeter and the with values. And so for the light. So we&#x27;ll end up with 294 equals two times 57 plus Teoh l two times 57 is 1 14 So we have to 94 equals 1 14 plus two l subtract 1 14 from both sides. How we get 1 80 equals two l The Bible says by two and we get l equals nineties centimeters. Uh oh.

James Kiss · Answer

all right from this information, we know that the length could be represented as three w plus eight because the length is three times the width and eight more. We also are given that the perimeter is 624. We know that perimeter is equal to twice the length, plus twice the width. And so let&#x27;s do some substituting. Um, we know that then 6 24 would be equal to two times the length, which is three W plus eight close to W. We can now distribute distribute, too, and now we had 6 24 equals two times three W, which is six w in two times eight, which is 16 plus two w. We can combine our like terms since around the same side of the equation six w close to W is a w. So now we had 6 24 He was eight. W bus 16. We can now subtract 16 double sides 6 24 minus 16 is 608 equals eight w. And our last step would be to divide both sides by eight, which gives us a width of 76. The dimensions of the rectangle then would be found by taking the width, which is one of the dimensions, and then plugging that into the brain. Remember, the length was three times the wits, which is now 76 plus eight. Three times 76 plus eight is 236 so the whip is 76 and the length is 236.

Problem

The basketball team has played 21 games. The rati…

Problem 21 Hard Difficulty

The ratio of the length to the width of a rectangle is 7 : 3. The area of the rectangle is 336 square centimeters. What are the dimensions of the rectangle?

Answer

28 cm by 12 cm

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