Question

Find the area of an isosceles triangle with perimeter is 36 cm and the base is 16 cm.

Answer 1

Perimeter of triangle = a + b + c

36 = 2a + 16

2a = 36 - 16

2a = 20

a = `20/2`

a = 10

Here, It is given that,

a = equal sides = 10 cm

b = base = 16 cm

Area of is isoscles triangle = `"b"/4  sqrt(4"a"^2 - "b"^2)`

`= 16/4 sqrt(4 (10)^2 - (16)^2)`

`= 4 sqrt(4 xx 100 - 256)`

`= 4 sqrt(400 - 256)`

`= 4 sqrt144`

= `4 xx 12`

= 48 cm²