Question

the two hexagons shown below are similar. image not to scale what is the length of cd? 7 of 7 questi

Explanation:

Step1: Use the property of similar polygons

For similar polygons, the ratios of corresponding sides are equal. So, \(\frac{CD}{C'D'}=\frac{ED}{E'D'}\).

Step2: Substitute the known values

Let \(CD = x\). We know \(C'D'=\frac{5}{2}\), \(ED = 4\), and \(E'D'=6\). Then \(\frac{x}{\frac{5}{2}}=\frac{4}{6}\).

Step3: Solve the proportion

Cross - multiply: \(6x = 4\times\frac{5}{2}\).
Simplify the right - hand side: \(4\times\frac{5}{2}=10\). So, \(6x = 10\).
Then \(x=\frac{10}{6}=\frac{5}{3}\).

Answer:

\(\frac{5}{3}\)