Question

the pentagons abcde and pqrst are similar. find the length x of \\( \overline { p q } \\).

Explanation:

Step1: Determine the scale factor

Since the pentagons are similar, the ratio of corresponding sides is equal. Consider the sides \(CD = 3\) and \(RS=2.7\). The scale factor \(k\) from pentagon \(ABCDE\) to \(PQ RST\) is \(k=\frac{RS}{CD}=\frac{2.7}{3}=0.9\).

Step2: Find the length of \(x\)

The side \(AB = 2\) in pentagon \(ABCDE\) corresponds to \(PQ=x\) in pentagon \(PQ RST\). Using the scale - factor formula \(x = AB\times k\). Substitute \(AB = 2\) and \(k = 0.9\) into the formula: \(x=2\times0.9\).

Answer:

\(x = 1.8\)