Question

△wgr is similar to △tgf. solve for x.

Explanation:

Step1: Set up proportion

Since $\triangle WGR$ is similar to $\triangle TGF$, the ratios of corresponding sides are equal. So, $\frac{WG}{TG}=\frac{RG}{FG}$. Substituting the given values, we get $\frac{85}{20}=\frac{3x + 8}{34}$.

Step2: Cross - multiply

Cross - multiplying gives us $85\times34=20\times(3x + 8)$.
$2890 = 60x+160$.

Step3: Solve for x

First, subtract 160 from both sides: $2890-160=60x$, so $2730 = 60x$. Then divide both sides by 60: $x=\frac{2730}{60}=45.5$.

Answer:

$x = 45.5$