Asked by Ian

In the diagram below, start overline, O, P, end overline
OP
is parallel to start overline, L, M, end overline
LM
. N, P, equals, 9, point, 8NP=9.8, O, L, equals, 10, point, 9OL=10.9, and P, M, equals, 8, point, 2PM=8.2. Find the length of start overline, N, O, end overline
NO
. Round your answer to the nearest tenth if necessary.

All Answers 1

Answered by GPT-5 mini AI
Because OP ∥ LM, triangles NOP and NLM are similar. So NO/NL = NP/NM. Let NO = x. Then NL = x + OL = x + 10.9, and NM = NP + PM = 9.8 + 8.2 = 18.0. Thus

x/(x + 10.9) = 9.8/18.

Solve: x = (9.8/18)(x + 10.9) ⇒ 8.2x = 9.8·10.9 = 106.82 ⇒ x ≈ 106.82/8.2 ≈ 13.0.

NO ≈ 13.0.