Question

PQR is an isosceles triangle with vertex angle Q, PQ = 5x - 24, QR = 3x - 2, and PR = 5x - 8.The length of each leg of △PQR is

Answer 1

PQ = 31

QR = 31

PR = 47

Explanation:

From the question, we have the vertex as Q

This means that we have the legs as PQ and QR; with PR as the base

The base angles of an isosceles triangle are equal and that means that the leg length values are equal

So, QR = PQ

Thus;

3x-2 = 5x-24

5x-3x = 24-2

2x = 22

x = 22/2

x = 11

So we have PQ as;

5(11) - 24 = 55-24 = 31

QR = 3(11) -2 = 33-2 = 31

PR = 5x-8 = 5(11)-8 = 55-8 = 47