Question

The perimeter of ΔPQR is 42, PQ = 12, Δ PQR ~ ΔSTU, and ST =24. What is the perimeter of ΔSTU? A) 60 B) 84 C) not enough information D) 46

Answer 1

Answer:

B) 84

Explanation:

If ΔPQR is similar to ΔSTU, then the ratio of corresponding sides is:

$\frac{PQ}{ST}=\frac{QR}{TU}=\frac{PR}{SU}$

• We are given PQ and ST.

,

• The ratio of corresponding sides is equal to the ratio of the perimeters.

$\begin{gathered} \frac{PQ}{ST}=\frac{\text{Perimeter of }\Delta PQR}{\text{Perimeter of }\Delta STU} \\ \frac{12}{24}=\frac{\text{4}2}{\text{Perimeter of }\Delta STU} \\ \frac{1}{2}=\frac{\text{4}2}{\text{Perimeter of }ΔSTU} \\ \text{Perimeter of }\Delta STU=42\times2 \\ \text{Perimeter of }\Delta STU=84\text{ units} \end{gathered}$