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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?

28 cm by 12 cm

Algebra

Chapter 2

THE RATIONAL NUMBERS

Section 5

Ratio and Proportion

Fractions and Mixed Numbers

Decimals

Equations and Inequalities

Harvey Mudd College

Baylor University

University of Michigan - Ann Arbor

Lectures

01:32

In mathematics, the absolu…

01:11

02:09

The length of a rectangle …

01:54

The ratio of the length to…

04:25

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02:25

01:40

The width of a rectangle i…

01:46

Geometry The length of a r…

03:05

Perimeter of a rectangle. …

04:18

Geometry The area of a rec…

01:31

So in this problem, what we'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'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't know that scale factor that we would multiply both terms by what we're going to do is call that X. So we're gonna write rewrite our ratio in the form of seven X to three X. So now we're gonna substitute seven X and for El and three X and for W. And then we'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'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'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's our scale faster and our length and width can'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'll have 12 centimeters, so our dimensions are 28 centime

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