Question

△PQR ≅ △XYZ, PQ = 3a + 4, and XY = 5a - 12. Find a and PQ.

A. a = 4, PQ = 16
B. a = 2, PQ = 10
C. a = 6, PQ = 22
D. a = 8, PQ = 28

Answer 1

Set the expressions for the congruent sides PQ and XY equal to each other and solve for 'a'. With 'a' found, calculate the length of PQ. The correct answer is D. a = 8, PQ = 28.

Step-by-step explanation:

The student asks to find the value of 'a' and the length of PQ given that triangles △PQR and △XYZ are congruent with sides PQ and XY represented as 3a + 4 and 5a - 12, respectively. To solve this, set the expressions for PQ and XY equal to each other, as the corresponding sides of congruent triangles are equal. This results in 3a + 4 = 5a - 12.

Solving the equation:

1. Subtract 3a from both sides: 4 = 2a - 12.
2. Add 12 to both sides: 16 = 2a.
3. Divide both sides by 2 to find a: a = 8.

Now, plug the value of a back into the expression for PQ to find its length:

PQ = 3a + 4 = 3(8) + 4 = 24 + 4 = PQ = 28.

Therefore, the correct answer is D. a = 8, PQ = 28.