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

B) 84

Step-by-step explanation:

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

`(PQ)/(ST)=(QR)/(TU)=(PR)/(SU)`

• We are given PQ and ST.

,

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

`\begin{gathered} (PQ)/(ST)=\frac{\text{Perimeter of }\Delta PQR}{\text{Perimeter of }\Delta STU} \\ (12)/(24)=\frac{\text{4}2}{\text{Perimeter of }\Delta STU} \\ (1)/(2)=\frac{\text{4}2}{\text{Perimeter of }ΔSTU} \\ \text{Perimeter of }\Delta STU=42*2 \\ \text{Perimeter of }\Delta STU=84\text{ units} \end{gathered}`