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In the diagram below of triangle MNO, P is the midpoint of MO and Q is the midpoint of NO. If PQ = 5x + 62, and MN = 6x-4, what is the measure of PQ?

In the diagram below of triangle MNO P is the midpoint of MO and Q is the midpoint of NO If PQ 5x 62 and MN 6x4 what is the measure of PQ class=

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Answer:

29

Step-by-step explanation:

There is a triangle embedded in triangle MNO, which is triangle PQO, and these are similar triangles in that their corresponding sides are always in the same ratio, which in this case is 2:1, as MP = MO due to the midpoint definition, and therefore MO is twice as long as MP. Same for NO and QO.

Now that we know the ratio, we can set 6x-4 = 2(-5x+64)

6x-4 = -10x +108

16x = 112

x = 7

Plug x back in for PQ, -5(7)+64 = 29

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