Question

How do I solve this? It’s on Khan Academy

Answer 1

AC being parallel to RP makes the triangles ABC and RBP similar. This means corresponding sides occur in the same ratio, so that

`(AC)/(RP)=(BC)/(BP)=(AB)/(RB)`

It's not clear from the picture what it is that you're supposed to find, but from the above relation we have

`(18)/(RP)=(BP+10)/(BP)=\frac{14+7}7`

From this it follows that

`(18)/(RP)=\frac{21}7=3\implies RP=\frac{18}3=6`

and

`(BP+10)/(BP)=\frac{21}7=3\implies BP+10=3BP\implies2BP=10\implies BP=5`