Question

∠NML≅∠NPO. P, M, equals, 8PM=8, N, O, equals, 28NO=28, and N, P, equals, 16NP=16. Find the length of start overline, O, L, end overline
OL
. Round your answer to the nearest tenth if necessary.
L
M
N
P
O


OL = what

Answer 1

Interpret the diagram so that M is between N and P and O is beyond P on the same line. Then NM = NP − PM = 16 − 8 = 8, and PO = NO − NP = 28 − 16 = 12.

Given ∠NML ≅ ∠NPO, triangles NML and NPO are similar with scale factor NM/NP = 8/16 = 1/2. Hence
NL = (1/2)·NO = (1/2)·28 = 14.

Since L and O lie on the same ray from N, OL = NO − NL = 28 − 14 = 14.

Answer: 14.