Question

△abc and △xyz are similar. find the missing side length.
(the triangles are not drawn to scale.)

Explanation:

Step1: Set up proportion

Since the triangles are similar, the ratios of corresponding sides are equal. Let the missing side be $x$. We have $\frac{AB}{XY}=\frac{AC}{XZ}=\frac{BC}{YZ}$. Using $\frac{AB}{XY}=\frac{AC}{XZ}$, we get $\frac{16}{x}=\frac{24}{3}$.

Step2: Cross - multiply

Cross - multiplying the proportion $\frac{16}{x}=\frac{24}{3}$ gives $24x = 16\times3$.

Step3: Solve for $x$

First, calculate $16\times3 = 48$. Then, $24x=48$. Divide both sides by 24: $x=\frac{48}{24}=2$.

Answer:

2