Question

In PQR, angle Q congruent angle R, If PQ = 10x - 14,
PR = 2x + 50, and RQ = 4x - 30, what is the length of RQ?

Answer 1

Answer:

RQ = 29

Step-by-step explanation:

The diagram of ∆PQR has been drawn to show the information given. See attachment below.

Since <Q is congruent to <R, it means the ∆PQR is an isosceles ∆ having two equal sides, PQ and PR.

Set the expression of the length PQ equal to that of PR to create an equation that will enable you to find the value of x.

Thus:

PQ = PR

10x - 14 = 2x + 50

Collect like terms

10x - 2x = 14 + 50

8x = 64

Divide both sides by 8

x = 64/8

x = 8

RQ = 4x - 3

Plug in the value of x

RQ = 4(8) - 3 = 32 - 3

RQ = 29