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In the diagram below of triangle OPQ, R is the midpoint of OQ and S is the
midpoint of PQ. If RS = 5x38, and OP = 7x - 49, what is the measure of
RS?

In the diagram below of triangle OPQ R is the midpoint of OQ and S is the midpoint of PQ If RS 5x38 and OP 7x 49 what is the measure of RS class=

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sqdancefan

Answer:

  RS = 7

Step-by-step explanation:

Given triangle OPQ with midsegment RS=5x-38 and parallel base segment OP=7x-49, we want the length of segment RS.

Setup

The midsegment is half the length of the base segment, so we have ...

  5x -38 = (1/2)(7x -49)

Solution

Multiplying by 2 gives ...

  10x -76 = 7x -49

  3x = 27 . . . . . . . . . . . add 76-7x

  x = 9 . . . . . . . . . . . divide by 3

  RS = 5x -38 = 5(9) -38 = 7

The length of RS is 7 units.

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