Question

I don't want a simple answer. I want to know how to do it.

Answer 1

The image is a bit hard to make out, so I'm going to make some guesses. It looks like it says
`PN=12`,
`QP=8`, and
`PM=17`, and you're asked to find
`QR`.

You know that
`\Delta NPM` and
`\Delta NQR` are similar, which means their corresponding sides are proportional in length. So there's some constant
`c` such that


`NP=cNQ`

`PM=cQR`

`MN=cRN`

To find
`QR`, you need to know
`PM` and the constant
`c`.

Clearly,
`NQ=NP+PQ=12+8=20`. So, the first equation becomes


`NP=cNQ\iff12=20c\implies c=(12)/(20)=\frac35`

Then in the second equation, you have


`17=\frac35QR\implies QR=17*\frac53=\frac{85}3=28.\overline3`