Question

triangles rst and uvw are similar. find the missing side x.

Explanation:

Step1: Set up proportion

Since the triangles are similar, the ratios of corresponding sides are equal. Let's assume the side of length 10 in $\triangle{RST}$ corresponds to the side of length 14.5 in $\triangle{UVW}$, and the side of length $x$ in $\triangle{RST}$ corresponds to the side of length 18.85 in $\triangle{UVW}$. The proportion is $\frac{10}{14.5}=\frac{x}{18.85}$.

Step2: Cross - multiply

Cross - multiplying gives us $14.5x = 10\times18.85$.

Step3: Solve for x

First, calculate $10\times18.85 = 188.5$. Then $x=\frac{188.5}{14.5}$.
$x = 13$

Answer:

$13$