Question

1. ab = ____________

Explanation:

Step1: Identify similar - triangles

Since $BD\parallel AE$, $\triangle CBD\sim\triangle CAE$.

Step2: Set up proportion

The ratio of corresponding sides of similar triangles is equal. Let $AB = x$, then $\frac{CB}{CA}=\frac{CD}{CE}$. Here, $CB = 18$, $CA=18 + x$, $CD = 24$, $CE=24 + 20=44$. So, $\frac{18}{18 + x}=\frac{24}{44}$.

Step3: Cross - multiply

Cross - multiplying gives $18\times44=24\times(18 + x)$.

Step4: Expand and solve

$792=432+24x$. Subtract 432 from both sides: $792 - 432=24x$, so $360 = 24x$. Then $x=\frac{360}{24}=15$.

Answer:

$15$