Question

The perimeter of isosceles triangle is 32. The ratio of the equal side to its base is 3:2. Find the area of the triangle. ​

Answer 1

Answer

Ratio of equal side to base = 3 : 2

Let the equal side = 3x

So, base = 2x

Perimeter(Δ) = 32

⇒ 3x + 3x + 2x = 32

⇒ 8x = 32

⇒ x = 4.

Equal side = 3x = 3×4 = 12

Base = 2x = 2×4 = 8

The sides of the triangle are 12cm, 12cm and 8cm.

a = 12, b = 12, c = 8

s = (a + b + c)/2

⇒ s = (12 + 12 + 8)/2 = 32/2 = 16.

Area(Δ) = √s(s-a)(s-b)(s-c)

⇒ Area(Δ) = √16(16-12)(16-12)(16-8)

⇒ Area(Δ) = √16×4×4×8

⇒ Area(Δ) = 32√2 cm2

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