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 $\frac{15}{x - 4}=\frac{12}{8}$.

Step2: Cross - multiply

Cross - multiplying gives us $15\times8 = 12\times(x - 4)$.

Step3: Simplify equation

$120=12x-48$.

Step4: Solve for x

Add 48 to both sides: $120 + 48=12x$, so $168 = 12x$. Then divide both sides by 12: $x = 14$.

Answer:

The proportion to solve for $x$ is $\frac{15}{x - 4}=\frac{12}{8}$ and $x = 14$.