ΔABC is similar to Δ PQR. AB = 4 cm , BC = 8 cm and AC = 10 cm . If QR = 16 cm, then what is the area of ΔPQR in cm2 ?

Explanation

Given: ΔABC is similar to ΔPQR. Length of sides in ΔABC: AB = 4 cm, BC = 8 cm, AC = 10 cm. QR = 16 cm in ΔPQR. Concept Used: The ratio of the areas of two similar triangles is equal to the square of the ratio of their corresponding sides. Area of scalene triangle = √s(s - a)(s - b)(s - c), where s = semi perimeter = sum of sides/2, and a, b, c are the sides of triangle. Solution: For ΔABC and ΔPQR, since ΔABC ~ ΔPQR, the ratio of corresponding sides QR/BC = 16/8 = 2. The ratio of the areas of ΔABC and ΔPQR will be the square of the ratio of their corresponding sides. ⇒ Area(ΔPQR)/Area(ΔABC) = (QR/BC)² = 2² = 4. Now the area of ΔABC ⇒ s = (4 + 8 + 10)/2 = 11 cm ⇒ Area of ΔABC = √11(11 - 4)(11 - 8)(11 - 10) ⇒ √11 × 7 × 3 × 1 = √231 cm2 Area of ΔPQR = 4 × Area of ΔABC = 4√231 cm2 ∴ Option 2 is the correct answer.