Question

the base of an isosceles triangle is 24 cm and its area is 102 cm square find the perimeter. heron's formula

Answer 1

Answer:

s= (a+b+c)/2

area = sqrt(s(s-a)(s-b)(s-c))

a=b=x

c=24

s =(2x+24)/2

s= x+12

Now, plug that in the formula.

sqrt((x+12)(x+12-x)^2(x+12-24)) = 102

sqrt((x+12)(12)^2(x-12)) =102

sqrt((x^2-144)(144) =102

144x^2-144^2=102^2

x= sqrt((102^2+144^2)/144))

x= 14.7

perimeter = 2*14.7+24

=53.4 cm