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

$\dfrac{AC}{RP}=\dfrac{BC}{BP}=\dfrac{AB}{RB}$

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

$\dfrac{18}{RP}=\dfrac{BP+10}{BP}=\dfrac{14+7}7$

From this it follows that

$\dfrac{18}{RP}=\dfrac{21}7=3\implies RP=\dfrac{18}3=6$

and

$\dfrac{BP+10}{BP}=\dfrac{21}7=3\implies BP+10=3BP\implies2BP=10\implies BP=5$