Question

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.
L
M
N
P
O

NO= what

Answer 1

Interpret LNM as a triangle with O on LN and P on MN, and OP ∥ LM. By the Triangle Proportionality Theorem,
LO/LN = MP/MN.

MN = MP + PN = 8.2 + 9.8 = 18.0, so
LN = LO * MN / MP = 10.9 * 18 / 8.2 ≈ 23.9268.

Then NO = LN − LO ≈ 23.9268 − 10.9 = 13.0268 ≈ 13.0 (to the nearest tenth).

Answer: 13.0