Question

Which of the following is the value of PQ ? Helllp please

Answer 1

Answer:

B. 61

Step-by-step 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

$\frac{40}{4} = \frac{4x}{4}$

$10 = x$

$x = 10$

Find PQ:

$PQ = 2x + 41$

substitute x = 10 into the equation

$PQ = 2(10) + 41$

$PQ = 20 + 41$

$PQ = 61$