Question

use the given triangles to answer the question.
△fgh is similar to △pqr.

• not drawn to scale

what is the length of \\(\overline{pr}\\)?
a. 3 cm
b. 4 cm
c. 7 cm
d. 9 cm

Explanation:

Step1: Identify Corresponding Sides

Since $\triangle FGH \sim \triangle PQR$, corresponding sides are proportional. Side $GH$ (10 cm) in $\triangle FGH$ corresponds to side $RQ$ (5 cm) in $\triangle PQR$, and side $FH$ (14 cm) in $\triangle FGH$ corresponds to side $PR$ in $\triangle PQR$.

Step2: Set Up Proportion

Let the length of $\overline{PR}$ be $x$. The ratio of corresponding sides is $\frac{GH}{RQ} = \frac{FH}{PR}$. Substituting values: $\frac{10}{5} = \frac{14}{x}$.

Step3: Solve for $x$

Simplify $\frac{10}{5} = 2$, so $2 = \frac{14}{x}$. Cross - multiply: $2x = 14$. Divide both sides by 2: $x = 7$.

Answer:

C. 7 cm