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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.
Solution
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,
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