Question

the base of an isosceles triangle is 24 cm and its area is 192 sq.cm. Find its perimeter

Answer 1

area of triangle=1/2*base*height
height=(2*192)/24
=16
So side=hypotenuse=x
x square=12square+16square
x square=400
x=√400
x=20
In an isosceles triangle the sides excluding the base are equal.
So perimeter=20+20+24
=64

Answer 2

Base of isosceles triangle (b) = 24cm

Area of isosceles triangle = 1/2× b under root 4a² - b²

192 = b under root 4a² - b²/2

192 = 24 under root 4 × a² - (24)²/ 2

192 = 24 under root 4a² - 576 / 2

192 = 24 × 2a - 24 / 2

192 = 24a

a = 192/24 = 8cm

Two sides of isosceles triangle are equal.

Hence,

the perimeter of isosceles triangle = a+ a + b

= 8+8+24 = 40cm