Question

Two triangles have their sides measuring 5cm, 6cm, 9cm and 7.5cm, 13.5cm, 20.25cm respectively. there areas are in the ratio:
a)2:3 b)4:9 c)9:4 d)3:2​

Answer 1

Answer:

a = 5cm, b = 6cm, c = 9 cm; s = (a + b + c) / 2 = 10cm.

a = 5cm, b = 6cm, c = 9 cm; s = (a + b + c) / 2 = 10cm.Area of this triangle = √{s * (s - a) * (s - b) * (s - c)} = √(10 * 5 * 4 * 1) sq cm = √200 sq cm = 14.142 sq cm

a = 5cm, b = 6cm, c = 9 cm; s = (a + b + c) / 2 = 10cm.Area of this triangle = √{s * (s - a) * (s - b) * (s - c)} = √(10 * 5 * 4 * 1) sq cm = √200 sq cm = 14.142 sq cmA = 7.5cm, b = 13.5cm, C = 20.25cm; S = (A + B + C) / 2 = 20.625cm.

a = 5cm, b = 6cm, c = 9 cm; s = (a + b + c) / 2 = 10cm.Area of this triangle = √{s * (s - a) * (s - b) * (s - c)} = √(10 * 5 * 4 * 1) sq cm = √200 sq cm = 14.142 sq cmA = 7.5cm, b = 13.5cm, C = 20.25cm; S = (A + B + C) / 2 = 20.625cm.Area of this triangle = √{S * (S - A) * (S - B) * (S - C)} = √(20.625 * 13.125 * 7.125 * 0.375) sq cm = √723.285 sq cm = 26.894 sq cm

a = 5cm, b = 6cm, c = 9 cm; s = (a + b + c) / 2 = 10cm.Area of this triangle = √{s * (s - a) * (s - b) * (s - c)} = √(10 * 5 * 4 * 1) sq cm = √200 sq cm = 14.142 sq cmA = 7.5cm, b = 13.5cm, C = 20.25cm; S = (A + B + C) / 2 = 20.625cm.Area of this triangle = √{S * (S - A) * (S - B) * (S - C)} = √(20.625 * 13.125 * 7.125 * 0.375) sq cm = √723.285 sq cm = 26.894 sq cmRatio of their areas = 10 : 19 (approximately).