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Question
If ΔPQR ∼ ΔABC; PQ = 6 cm, AB = 8 cm and the perimeter of ΔABC is 36 cm, then the perimeter of ΔPQR is ______.
Options
20.25 cm
27 cm
48 cm
64 cm
Solution
If ΔPQR ∼ ΔABC; PQ = 6 cm, AB = 8 cm and the perimeter of ΔABC is 36 cm, then the perimeter of ΔPQR is 27 cm.
Explanation:
∵ Ratio of side = Ratio of perimeter
`\implies (PQ)/(AB) = ("Perimeter of" ΔPQR)/("Perimeter of" ΔABC)`
`\implies 6/8 = ("Perimeter of" ΔPQR)/36`
`\implies 3/4 = ("Perimeter of" ΔPQR)/36`
`\implies` Perimeter of ΔPQR = `(36 xx 3)/4`
= 9 × 3
= 27 cm
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