Question

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

Answer 1

Perimeter = 32
Ratio of equal side to its base = 3:2
Perimeter = 3x + 2x
           32  =  5x
              x = 32 / 5
              x = 6.4
3x = 3 x 6.4 = 19.2
2x = 2 x 6.4 =12.8
base = 12.8cm
sum of 2 equal sides = 19.2 / 2 = 9.6cm
By Heron's formula,
                              [s(s-a)(s-b)(s-c)]
s = 32 / 2 = 16
                              [16(16-9.6)(16-9.6)(16-12.8)]
                           = [16(6.4)(6.4)(3.2)]
                           = 6.4 to the root of [16 x 3.2]
                           = 6.4 to the root of 51.2
                           = 45.8 sq.cm.