Question

In the diagram of LPN below, QM||PN,LQ=6,LM=11, and MN=22. What is the length of LP

Answer 1

LP=18

Step-by-step explanation:

To find the length of LP, we use the Triangle Proportionality Theorem.

Applying this to LPN, we have:

`(LQ)/(QP)=(LM)/(MN)`

Substituting the given values, we have:

`\begin{gathered} (6)/(PQ)=(11)/(22) \\ (6)/(PQ)=(1)/(2) \\ PQ=6*2 \\ PQ=12 \end{gathered}`

Therefore:

`\begin{gathered} LP=LQ+PQ \\ =6+12 \\ =18\text{ units} \end{gathered}`