Asked by Toxic

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
OP || LN implies triangles MOP and MLN are similar, so MO/ML = MP/MN.

MO = 28, ML = 28 + 14 = 42, MP = y, MN = y + 18. Thus
28/42 = y/(y+18) => 2/3 = y/(y+18) => 2y + 36 = 3y => y = 36.

Answer: 36.