Question

triangle bcd is similar to triangle efg. find fg. round your answer to the nearest tenth if necessary. figures are not drawn to scale.

Explanation:

Step1: Identify corresponding sides

Since $\triangle BCD \sim \triangle EFG$, the corresponding sides are proportional. Let's assume $BC$ corresponds to $EF$, and $CD$ corresponds to $FG$. So, $BC = 9$, $CD = 5$, $EF = 35$, and $FG = x$.

Step2: Set up proportion

The proportion for similar triangles is $\frac{BC}{EF}=\frac{CD}{FG}$. Substituting the known values, we get $\frac{9}{35}=\frac{5}{x}$.

Step3: Solve for x

Cross - multiply: $9x = 35\times5$.
Calculate $35\times5 = 175$. So, $9x = 175$.
Then, $x=\frac{175}{9}\approx19.4$ (rounded to the nearest tenth).

Answer:

$\approx19.4$