Question

In the diagram below, OP is parallel to LM. If NP = 7, LM = 7.2, LN =

and OP= 6, find the length of NM. Figures are not necessarily drawn to scale.

Answer 1

8.4

Explanation:

`\angle PON \cong \angle NLM` and
`\angle OPN \cong \angle NML` because they are alternate interior angles. Thus, the triangles are similar by angle-angle.

Corresponding sides of similar triangles have proportional side lengths, so:

`(NM)/(7)=(7.2)/(6) \\ \\ NM=8.4`

Answer 2

The length of NM from the figure drawn is 8.4

Setting up a proportional relationship thus ;

NM = NP

LM = OP

Substituting the values ;

NM = 7

7.2 = 6

Cross multiply

6NM = 7 × 7.2

6NM = 50.4

NM = 50.4/6

NM = 8.4

Therefore, the length of NM is 8.4 units