Question

In triangle MNP, medians NQ and PR intersect at S. If PS = 8 and QS = 3 then which of the following is the value of NQ + PR

(1) 21
(2) 22
(3) 26
(4) 30

Answer 1

(2) 22

Explanation:

In the given triangle MNP, the medians are straight lines drawn from the angle to opposite side so as to divide the side into equal parts.

PS = 8 and QS = 3, thus;

PS = NS = 8 (congruent property of ΔRSN and ΔQSP)

QS = SP = 3 (congruence property)

So that,

NQ = NS + SQ

= 8 + 3

= 11

PR = PS + SR

= 8 + 3

= 11

Thus;

NQ + PR = 11 + 11

= 22

Therefore, NQ + PR = 22