Question

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

Answer 1

here we use hero formula
s=(a+b+c)/2
but triangle is isoceles so, a=b and c=24cm
s=(a+a+24)/2=(a+12 ) cm
now area of triangle=root {s (s-a)(s-b)(s-c)}

192cm^2=root {(a+12)((a+12-a)(a+12-a)(a+12-24)}
192 cm^2=12 root{ (a+12)(a-12)}
16=root (a^2-144)
squaring both side
256=a^2-144
a^2=400
a=20,-20
but -20 isn't possible
hence a=20cm
because a=b
so, b=20cm
now perimeter of triangle=(20+20+24)=64cm

Answer 2

answer is 64 cm.............