Question

In the diagram below, NO is parallel to KL. If LO = 4, NO = 3, and KL = 6, find the

length of MO. Figures are not necessarily drawn to scale. State your answer in simplest radical
form, if necessary.
K
N
M

Answer 1

Based on triangle KLM, the length of MO include the following: 4 units.

In Mathematics and Euclidean Geometry, the basic proportionality theorem states that when any of the two sides of a triangle is intersected by a straight line which is parallel to the third side of the triangle, then, the two sides that are intersected would be divided proportionally and in constant ratio.

Note: ML = MO + LO

By applying the basic proportionality theorem to isosceles triangle KLM, we have the following proportional side lengths:

MO/(MO + LO) = NO/KL

MO/(MO + 4) = 3/6

3(MO + 4) = 6MO

MO + 4 = 2MO

2MO - MO = 4

MO = 4 units.