Question

1. (3 points) below are two rectangles. if ( ab = 8 ), ( bc = 12 ), ( uv = 18 ), and ( vw = 24 ), determine whether or not the two rectangles are similar. justify your decision.

Explanation:

Step1: Calculate the ratios of corresponding sides

For the first rectangle \(ABCD\), sides are \(AB = 8\) and \(BC=12\). For the second rectangle \(UVWX\), sides are \(UV = 18\) and \(VW = 24\).
The ratio of the shorter sides: \(\frac{AB}{UV}=\frac{8}{18}=\frac{4}{9}\)
The ratio of the longer sides: \(\frac{BC}{VW}=\frac{12}{24}=\frac{1}{2}\)

Step2: Compare the ratios

Since \(\frac{4}{9}
eq\frac{1}{2}\) (because \(4\times2 = 8\) and \(9\times1=9\), \(8
eq9\)), the ratios of the corresponding sides of the two rectangles are not equal.

Answer:

The two rectangles are not similar. Because the ratios of their corresponding sides (\(\frac{AB}{UV}=\frac{4}{9}\) and \(\frac{BC}{VW}=\frac{1}{2}\)) are not equal.