Question

When triangle ABC is similar to triangle PQR, with A, B, and C corresponding to P, Q, and R, respectively, it is customary to write ABC ∼ PQR. Suppose that AB = 4, BC = 5, CA = 6, and RP = 9. Find PQ and QR.

Answer 1

PQ = 6 and QR = 7.5

Explanation:

The lengths of the sides of two similar triangles are proportional. That is, if Δ ABC is similar to Δ PQR, then the following equation is established.

`(AC)/(PR)=(AB)/(PQ)=(BC)/(QR)`

`(6)/(9) = (4)/(PQ) = (5)/(QR)`

`(6)/(9) = (4)/(PQ)`

PQ = 6

`(6)/(9) = (5)/(QR)`

QR = 7.5