Question

the figures below are similar. the labeled sides are corresponding.

red rectangle with bottom side labeled 6 yd blue rectangle with bottom side labeled u

if the ratio of the rectangles perimeters is 6:1, what is u?

u = \boxed{} yards

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Explanation:

Step1: Use the property of similar figures

For similar figures, the ratio of their perimeters is equal to the ratio of their corresponding side lengths.
Let the ratio of perimeters \(P_1:P_2 = 6:1\). Let the corresponding side lengths be \(s_1 = 6\) yd and \(s_2=u\). Then \(\frac{P_1}{P_2}=\frac{s_1}{s_2}\).

Step2: Substitute values into the proportion

Substitute \(P_1:P_2 = 6:1\) (so \(\frac{P_1}{P_2}=6\)) and \(s_1 = 6\), \(s_2 = u\) into \(\frac{P_1}{P_2}=\frac{s_1}{s_2}\). We get \(6=\frac{6}{u}\).

Step3: Solve for \(u\)

Cross - multiply: \(6u=6\). Then divide both sides by 6: \(u = 1\).

Answer:

\(1\)