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