Question

△jkl and △pqr are congruent isosceles triangles. find pq. (not drawn to scale) a 5 b 10 c 12 d 15

Explanation:

Step1: Use congruence property

Since $\triangle{JKL}$ and $\triangle{PQR}$ are congruent, corresponding sides are equal. Assume $PQ = JL$. So $3x=5x - 10$.

Step2: Solve the equation for $x$

Subtract $3x$ from both sides: $0 = 5x-3x - 10$, which simplifies to $0 = 2x - 10$. Then add 10 to both sides: $10=2x$. Divide both sides by 2, we get $x = 5$.

Step3: Find $PQ$

Substitute $x = 5$ into the expression for $PQ$. Since $PQ=3x$, then $PQ=3\times5 = 15$.

Answer:

D. 15