Question

How do i do this problem liek i have to find a side?

Answer 1

`\overline{LP}=77`

Explanation:

Given
`\Delta LMQ\sim\Delta LNP`, then
`\overline{LN}=\overline{LM}+\overline{MN}=8+14=22`. This will help us find
`\overline{LQ}` since we know the length of
`\overline{QP}`:

`\displaystyle \frac{\overline{LM}}{\overline{LM}+\overline{MN}}=\frac{\overline{LQ}}{\overline{LQ}+\overline{QP}}\\\\(8)/(8+14)=\frac{\overline{LQ}}{\overline{LQ}+49}\\\\(8)/(22)=\frac{\overline{LQ}}{\overline{LQ}+49}\\\\8(\overline{LQ}+49)=22\overline{LQ}\\\\8\overline{LQ}+392=22\overline{LQ}\\\\392=14\overline{LQ}\\\\28=\overline{LQ}`

Therefore:

`\overline{LP}=\overline{LQ}+\overline{QP}=28+49=77`