Question

In the diagram below of triangle O, P, QOPQ, RR is the midpoint of start overline, O, Q, end overline
OQ
​
and SS is the midpoint of start overline, P, Q, end overline
PQ
​
. If R, S, equals, 8, x, minus, 66RS=8x−66, and O, P, equals, minus, 4, x, plus, 48OP=−4x+48, what is the measure of start overline, O, P, end overline
OP
?

Answer 1

R and S are midpoints, so RS is the midsegment parallel to OP and RS = (1/2)·OP.

Set 8x − 66 = (1/2)(−4x + 48).
8x − 66 = −2x + 24
10x = 90 → x = 9.

Then OP = −4x + 48 = −36 + 48 = 12.

So the length of OP is 12.