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| Math Central | Quandaries & Queries |
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Question from Alyssa, a student: The ratio of the lengths of corresponding sides of two similar rectangles is 3:5. the small rectangle has an area of 36 square centimeters. What is the are of the large rectangle? |
Alyssa,
Divide the length of the small rectangle by 3. You get some number x. Thus the length of the small rectangle is 3x centimeters.
Divide the width of the small rectangle by 3. You get some number y. Thus the width of the small rectangle is 3y centimeters.
Hence the area of the small rectangle is 3x × 3y = 9xy square centimeters. But you know the area is 36 square centimeters so what is xy?
The ratio of the lengths of corresponding sides of the two rectangles is 3:5. The length of the small rectangle is 3x centimeters, what is the length of the large rectangle? What is its width? What is its area?
Penny
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