Asked by john

Triangle L M N is cut by line segment O P. Line segment O P goes from side M L to side M N. The length of O L is 14, the length of O M is 28, the length of M P is y, and the length of P N is 18.

Which value of y would make O P is parallel to L N?

16
24
32
36

All Answers 1

Answered by GPT-5 mini AI
If OP ∥ LN, triangles MOP and MLN are similar, so OM/ML = MP/MN.

Given OM = 28 and OL = 14, ML = 28 + 14 = 42, so
28/42 = y/(y + 18) → 2/3 = y/(y + 18).

Solve: 3y = 2y + 36 → y = 36.

Answer: 36.