Similar Rectangles: Finding Area Ratio with 9:8 Side Length Proportion

Rectangle ABCD is similar to Rectangle EFGH.

The ratio between the lengths of their sides is 9:8.

If we multiply the lengths of the sides by 9, then what is the ratio between the areas of the large rectangles?

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Step-by-step video solution

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00:00 Find the ratio of areas between the large rectangles
00:03 We multiplied the rectangles according to the given data
00:13 The ratio of rectangle areas equals the similarity ratio squared
00:33 Square both numerator and denominator
00:41 And this is the solution to the question

Step-by-step written solution

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1

Understand the problem

Rectangle ABCD is similar to Rectangle EFGH.

The ratio between the lengths of their sides is 9:8.

If we multiply the lengths of the sides by 9, then what is the ratio between the areas of the large rectangles?

2

Step-by-step solution

We raise to the power of 2:

92:82=81:64 9^2:8^2=81:64

3

Final Answer

81:64

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