Question

ΔABC ~ ΔPQR. In ΔABC, AB = 5.4 cm, BC = 4.2 cm, AC = 6.0 cm, AB:PQ = 3:2, then construct ΔABC and ΔPQR.

Answer 1

ΔABC ~ ΔPQR  ......[Given]

We know that corresponding sides of triangle which are similar are in proportion

∴ `("AB")/("PQ") = ("BC")/("QR") = ("AC")/("PR") = 3/2`

∴ `("AB")/("PQ") = 3/2`

∴ `5.4/("PQ") = 3/2`

∴ PQ = `(5.4 xx 2)/3`

∴ PQ = 3.6 cm

Also, `("BC")/("QR") = 3/2`

∴ `4.2/("Q") = 3/2`

∴ QR = `(4.2 xx 2)/3`

∴ QR = 2.8 cm

Also, `("AC")/("PR") = 3/2`

∴ `6/("PR") = 3/2`

∴ PR = `(6 xx 2)/3`

∴ PR = 4 cm

Now, draw angle ΔABC with sides AB = 5.4 cm, BC = 4.2 cm and AC = 6 cm.

Also draw triangle ΔPQR with sides PQ = 3.6 cm, QR = 2.8 cm and PR = 4 cm.

ΔABC,

ΔPQR,