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

Answer 1

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