Question

abcd ~ fecg
x = ?

Explanation:

Step1: Use property of similar polygons

For similar polygons, the ratios of corresponding - sides are equal. Since \(ABCD\sim FECG\), the ratio of corresponding sides is the same. We can set up the proportion using the sides \(AB\) and \(FE\), \(BC\) and \(EC\). The proportion is \(\frac{AB}{FE}=\frac{BC}{EC}\).

Step2: Substitute known values

We know that \(BC = 5\), \(EC = 5\), and \(FE = 6\). Let \(AB=x\). Substituting into the proportion \(\frac{x}{6}=\frac{5}{5}\).

Step3: Solve the proportion

Cross - multiply (in this case, since \(\frac{x}{6}=\frac{5}{5}=1\)), we get \(x = 6\).

Answer:

6