Question

1. the areas of two similar rectangles are 338 cm² and 72 cm². what is the ratio of their perimeters?

29:12
338:72
13:6
169:36

Explanation:

Step1: Recall the ratio of areas of similar figures

For similar figures, the ratio of their areas is equal to the square of the ratio of their corresponding side lengths. Let the ratio of side lengths be \(a:b\), then the ratio of areas is \(a^{2}:b^{2}\).

Step2: Simplify the given area ratio

Given areas \(A_1 = 338\) and \(A_2=72\). The ratio of areas is \(\frac{A_1}{A_2}=\frac{338}{72}\). Simplify \(\frac{338\div2}{72\div2}=\frac{169}{36}\)

Answer:

\(169:36\)