# Triangle ABC is similar to triangle PQR . AB corresponds to PQ and BC corresponds to QR. lf AB = 9, BC = 12, CA = 6, and PQ = 3, what are the lengths of QR and RP?

Jan 9, 2017

$Q R = 4$ and $R P = 2$

#### Explanation:

As $\Delta A B C \approx \Delta P Q R$ and $A B$ corresponds to $P Q$ and $B C$ corresponds to $Q R$, we have,

Then we have

$\frac{A B}{P Q} = \frac{B C}{Q R} = \frac{C A}{R P}$

Hence $\frac{9}{3} = \frac{12}{Q R} = \frac{6}{R P}$

i.e. $\frac{9}{3} = \frac{12}{Q R}$

or $Q R = \frac{3 \times 12}{9} = \frac{36}{9} = 4$

and $\frac{9}{3} = \frac{6}{R P}$

or $R P = \frac{3 \times 6}{9} = \frac{18}{9} = 2$