Question

Which of the following is the value of PQ ?

Helllp please

Answer 1

B. 61

Explanation:

Given that ∆PQR and PQS are congruent, it follows that their corresponding sides are of the same length.

Therefore,

`RQ = SQ`

`3x + 16 = 7x - 24`

Collect like terms

`16 + 24 = 7x - 3x`

`40 = 4x`

Divide both sides by 4

`(40)/(4) = (4x)/(4)`

`10 = x`

`x = 10`

Find PQ:

`PQ = 2x + 41`

substitute x = 10 into the equation

`PQ = 2(10) + 41`

`PQ = 20 + 41`

`PQ = 61`