Question

set up a proportion to solve for x in the following similar triangles.

Explanation:

Step1: Set up proportion

For similar triangles, the ratios of corresponding sides are equal. So we set up the proportion $\frac{24}{x - 2}=\frac{18}{12}$.

Step2: Cross - multiply

Cross - multiplying gives us $24\times12 = 18\times(x - 2)$.
$288=18x-36$.

Step3: Solve for x

Add 36 to both sides: $288 + 36=18x$, so $324 = 18x$.
Divide both sides by 18: $x=\frac{324}{18}=18$.

Answer:

$x = 18$