Question

ΔABC has sides of length 4 cm, 5 cm and 6 cm while ΔPQR has perimeter of 90 cm. If ΔABC is similar to ΔPQR, then find the length of corresponding sides of ΔPQR.

Answer 1

Let AB = 4 cm, BC = 5 cm and AC = 6 cm.

ΔABC ∼ ΔPQR   ...(Given)

∴ `"AB"/"PQ" = "BC"/"QR" = "AC"/"PR"`   ...(Corresponding sides of similar triangles)

∴ `4/"PQ" = 5/"QR" = 6/"PR"`

∴ By theorem on equal ratios, we get,

`4/"PQ" = 5/"QR" = 6/"PR" = (4 + 5 + 6)/("PQ" + "QR" + "PR")`

∴ `4/"PQ" = 5/"QR" = 6/"PR" = 15/90`   ...[∵ Perimeter of ΔPQR = 90]

∴ `4/"PQ" = 5/"QR" = 6/"PR" = 1/6`

∴ `4/"PQ" = 1/6`

∴ PQ = 4 × 6

∴ PQ = 24 cm

∴ `5/"QR" = 1/6`

∴ QR = 5 × 6

∴ QR = 30 cm

∴ `6/"PR" = 1/6`

∴ PR = 6 × 6

∴ PR = 36 cm

The sides of ΔPQR are 24 cm, 30 cm and 36 cm.