The base of an isosceles triangle is of length 48 cm and its. . .

Question : The base of an isosceles triangle is of length 48 cm and its area is 240 cm². Use Heron's formula and hence find the perimeter of the triangle.

Doubt by Veer

Solution : 

Here
a=48 cm 

b=x cm

c=x cm 

Semiperimeter (s) 

s=[a+b+c]/2
s=[48+x+x]/2
s=[48+2x]/2
s=2[24+x]/2
s=[24+x] cm 

Area = 240 cm² [Given]

√[s(s-a)(s-b)(s-c)] = 240
√[24+x(24+x-48)(24+x-x)(24+x-x)] = 240
√[24+x(x-24)(24)(24)] = 240
Squaring both sides
[(x+24)(x-24)24×24]=240×240
x²-(24)²=(240×240)/(24×24)
x²-576=100
x²=100+576
x²=676
x=√676
x=26

b=c=26 cm 

So, 
Perimeter of triangle
P=a+b+c
P=48+26+26
P=48+52
P=100 cm²