Question

in the diagram below, OP is parallel to LM. solve for x. round your answer to the nearest tenth if necessary.

Answer 1

With the given information we can conclude that triangles OPN and LMN are similar. Thus, the proportion between corresponding sides is equal, it means:

`(NO)/(OL)=(NP)/(PM)`

In the figure we can see that NO=4.4 OL=3.6 NP=3.3 and PM=x.

Replace these values and solve for x as follows:

`\begin{gathered} (4.4)/(3.6)=(3.3)/(x) \\ \text{Multiply both sides by x} \\ (4.4)/(3.6)\cdot x=(3.3)/(x)\cdot x \\ \text{Simplify} \\ (4.4)/(3.6)\cdot x=3.3 \\ \text{Multiply both sides by 3.6} \\ (4.4)/(3.6)\cdot3.6\cdot x=3.3\cdot3.6 \\ \text{Simplify} \\ 4.4x=11.88 \\ \text{Divide both sides by 4.4} \\ (4.4x)/(4.4)=(11.88)/(4.4) \\ \text{Simplify} \\ x=2.7 \end{gathered}`

Thus, x=2.7