Question

Δ ABC is similar to Δ PQR. If AB = 6cm, BC = 9cm, PQ = 9cm and PR = 10.5cm, find the lengths of AC and QR.

Answer 1

Given : Δ ABC ∼ Δ PQR

To find : AC and QR

Sol : Δ ABC ∼ Δ PQR

`therefore "AB"/"PQ" = "BC"/"QR" = "AC"/"PR"`  (Similar sides of similar triangles)

`6/9 = 9/"y" = "x"/10.5`

`6/9 = 9/"y"`                                   `6/9 = "x"/10.5`

⇒ 6y = 81                                      ⇒ 63 = 9x

⇒ y = `81/6`                                  ⇒ x = 7

⇒ y = `27/2`                                  ⇒ AC = 7 cm

⇒ QR = 13.5 cm