Question

each pair of polygons are similar. find the missing side length.

1. △abe ~ △cde

Explanation:

Step1: Set up the proportion

Since \(\triangle ABE\sim\triangle CDE\), the ratios of corresponding sides are equal. So, \(\frac{AB}{CD}=\frac{AE}{CE}\). Here, \(AB = 15\), \(CD=10\), \(CE = 12\), and \(AE=x\). The proportion is \(\frac{15}{10}=\frac{x}{12}\).

Step2: Cross - multiply

Cross - multiplying gives \(10x=15\times12\).

Step3: Solve for \(x\)

First, calculate \(15\times12 = 180\). Then, \(x=\frac{180}{10}\).

Answer:

\(x = 18\)