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,
[tex] RQ = SQ [/tex]
[tex] 3x + 16 = 7x - 24 [/tex]
Collect like terms
[tex] 16 + 24 = 7x - 3x [/tex]
[tex] 40 = 4x [/tex]
Divide both sides by 4
[tex] \frac{40}{4} = \frac{4x}{4} [/tex]
[tex] 10 = x [/tex]
[tex] x = 10 [/tex]
Find PQ:
[tex] PQ = 2x + 41 [/tex]
substitute x = 10 into the equation
[tex] PQ = 2(10) + 41 [/tex]
[tex] PQ = 20 + 41 [/tex]
[tex] PQ = 61 [/tex]
