Video: Finding the Area of a Rectangle Similar to Another given Their Side Lengths and the Area of the Second Rectangle

These two rectangles are similar. Given that the area of the yellow one is 69.3 cm², find the area of the green rectangle.

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Video Transcript

These two rectangles are similar. Given that the area of the yellow one is 69.3 square centimeters, find the area of the green rectangle.

So it’s important to know that these rectangles are similar. And we are given side lengths for each of them. So we can create a ratio, the smaller length to the larger length, which is seven to 14. Now if we are wanting to solve for an area, we don’t want to use a length ratio. We want to use an area ratio. And what we know about the area ratio is that it’s equal to the square of the length ratio. So if we would square the length ratio, we would have the area ratio.

So let’s go ahead and square our seven and the 14. So we have an area ratio of 49 to 196. And now we can set up a proportion to solve for the area of the green rectangle. Since 49 is smaller, it should go with the area of the smaller rectangle, which we know to be the yellow one. And its area is 69.3. And then the area of the larger rectangle we can call 𝑥.

So now we need to cross-multiply and solve. 49 times 𝑥 is 49𝑥. And 69.3 times 196 is equal to 13582.8. So now we need to divide both sides of the equation by 49. And we find that 𝑥 is equal to 277.2. This means the area of the larger rectangle, the green rectangle, is 277.2 square centimeters.

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