Questions: If triangle W V X is similar to triangle R T S, find x.

If $\triangle WVX \sim \triangle RTS$, find $x$.

Set up a proportion

Since $\triangle WVX \sim \triangle RTS$, the corresponding sides are proportional. Thus, we can set up the proportion: $\frac{WX}{RS} = \frac{VX}{TS}$

Substitute the given values

We are given $WX = 3x - 21$, $RS = x + 13$, $VX = 27 + WY = 27+27=54$, and $TS = 24+SU = 24+24 = 48$. Substituting these values into the proportion, we get: $\frac{3x - 21}{x + 13} = \frac{54}{48}$

Simplify the fraction

Simplify the fraction on the right side: $\frac{54}{48} = \frac{9}{8}$ So, the proportion becomes: $\frac{3x - 21}{x + 13} = \frac{9}{8}$

Cross-multiply

$8(3x - 21) = 9(x + 13)$ $24x - 168 = 9x + 117$

Solve for x

$24x - 9x = 117 + 168$ $15x = 285$ $x = \frac{285}{15}$ $x = 19$

$\boxed{x = 19}$

$\boxed{x = 19}$