Question

the triangles are similar. solve for x. 123 30 20 2x + 8 x = 37

Explanation:

Step1: Set up proportion

Since the triangles are similar, the ratios of corresponding sides are equal. So, $\frac{123}{30}=\frac{2x + 8}{20}$.

Step2: Cross - multiply

$123\times20=30\times(2x + 8)$.
$2460 = 60x+240$.

Step3: Isolate the variable term

Subtract 240 from both sides: $2460-240=60x$.
$2220 = 60x$.

Step4: Solve for x

Divide both sides by 60: $x=\frac{2220}{60}=37$.

Answer:

$x = 37$