Question

find x, the length of the line segment $overline{ab}$.

Explanation:

Step1: Identify similar triangles

Since $\triangle CDE$ and $\triangle CAB$ have equal - angled corresponding angles (by AA similarity, as $\angle C$ is common and $DE\parallel AB$), they are similar.

Step2: Set up proportion

For similar triangles $\triangle CDE$ and $\triangle CAB$, the ratios of their corresponding sides are equal. That is, $\frac{CD}{CA}=\frac{DE}{AB}$. Here, $CD = 11$, $CA=11 + 11=22$, and $DE = 8$. Let $AB=x$. So, $\frac{11}{22}=\frac{8}{x}$.

Step3: Solve the proportion

Cross - multiply the proportion $\frac{11}{22}=\frac{8}{x}$ to get $11x=22\times8$. Then $11x = 176$. Divide both sides by 11: $x=\frac{176}{11}=16$.

Answer:

$16$