Question

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?

Answer 1

RS = 7

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.