Question

The unequal sides of an isosceles triangle is $6cm$ & its perimeter $24cm$. Find its area.

Answer 1

Given that the unequal side $=6㎝$

Let equal side be y

Perimeter$=6+y+y$

Given perimeter $=24$

$6+2y=24$

$2y=18$

$y=9$

$AB=9,BC=6,CA=9$

$s=\frac{AB+BC+CA}{2}=\frac{9+9+6}{2}=12$

$s-a=12-9=3$

$s-b=12-6=6;s-c=12-9=3$

$△=\sqrt{s(s-a)(s-b)(s-c)}$

$=\sqrt{12\times 3\times 6\times 3}$

$=\sqrt{6\times 2\times 3\times 3\times 6}=3\times 6\times \sqrt{2}$

$△=18\sqrt{2}㎠$