R is the midpoint of PQ. PR = 6x + 7 and RQ = 3x + 8, find the length of PQ.

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Hamish Downer asked Apr 20, 2023

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R is the midpoint of PQ. PR = 6x + 7 and RQ = 3x + 8, find the length of PQ.

Mathematics
high-school

Hamish Downer asked Apr 20, 2023

by Hamish Downer

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28 votes

Answer:

PQ = 18

Explanation:

If R is the midpoint of PQ, then PR = RQ

⇒ 6x + 7 = 3x + 8

⇒ 3x = 1

⇒ x = 1/3

So PR = 6x + 7 = 6(1/3) + 7 = 9

and RQ = 3x + 8 = 3(1/3) + 8 = 9

⇒ PQ = PR + RQ = 9 + 9 = 18

Adam Link answered Apr 26, 2023

by Adam Link

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