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 the known values

We know that \(AB = x\), \(FE = 4\), \(BC = 5\), and \(EC = 6\). Substituting these values into the proportion \(\frac{AB}{FE}=\frac{BC}{EC}\), we get \(\frac{x}{4}=\frac{5}{6}\).

Step3: Solve for \(x\)

Cross - multiply the proportion \(\frac{x}{4}=\frac{5}{6}\) to get \(6x = 4\times5\), which simplifies to \(6x = 20\). Then \(x=\frac{20}{6}=\frac{10}{3}\).

Answer:

\(\frac{10}{3}\)