Question 12 Marks
An isosceles triangle has perimeter $30 \ cm$ and each of the equal sides is $12 \ cm$. Find the area of the triangle.
Answer
$a = 12 \ cm, b = 12 \ cm$
Perimeter $= 30 \ cm$
$a + b + c = 30$
$\Rightarrow 12 + 12 + c = 30$
$\Rightarrow 24 + c = 30$
$\Rightarrow c = 30 – 24$
$\Rightarrow c = 6 \ cm$
$s = \frac{30}{2} \ cm$
$ = 15 \ cm$
$\therefore$ Area of the $\triangle =\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{15(15-12)(15-12)(15-6)}$
$=\sqrt{15(3)(3)(9)}$
$=9\sqrt{15} \ cm^2$
View full question & answer→$a = 12 \ cm, b = 12 \ cm$
Perimeter $= 30 \ cm$
$a + b + c = 30$
$\Rightarrow 12 + 12 + c = 30$
$\Rightarrow 24 + c = 30$
$\Rightarrow c = 30 – 24$
$\Rightarrow c = 6 \ cm$
$s = \frac{30}{2} \ cm$
$ = 15 \ cm$
$\therefore$ Area of the $\triangle =\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{15(15-12)(15-12)(15-6)}$
$=\sqrt{15(3)(3)(9)}$
$=9\sqrt{15} \ cm^2$