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


4
1