In the diagram below, start overline, Q, R, end overline
QR
is parallel to start overline, N, O, end overline
NO
. If N, Q, equals, 20NQ=20, Q, R, equals, 24QR=24, and N, O, equals, 44NO=44, find the length of start overline, Q, P, end overline
QP
. Figures are not necessarily drawn to scale. State your answer in simplest radical form, if necessary.
Since QR is parallel to NO, we can use the similarity of triangles to find the length of QP.
We have the proportion: QP/NO = QR/NQ
Plugging in the given values: QP/44 = 24/20
Cross multiplying: QP*20 = 44*24
Simplifying: QP = (44*24)/20 = 11*24/5 = 264/5 = 52.8
Therefore, the length of QP is 52.8.