Question

The area of a triangle is $216c{m}^2$ and its sides are in the ratio 3 : 4 : 5 The perimeter of the triangle is

• A. 6 cm
• B. 12 cm
• C. 36 cm
• D. 72 cm

Answer 1

The correct option is D 72 cm

Let the sides of the triangle be $3xcm,4xcm$ and 5x cm Then
$s=\frac{3x+4x+5x}{2}=\frac{12x}{2}=6x$
$\therefore$ Area of $\Delta =\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{6x(6x-3)(6x-4x)(6x-5x)}$
$=\sqrt{6x\times 3x\times 2x\times x=6x^2}$
Given $6x^2=216\Rightarrow x^2=\frac{216}{6}=36\Rightarrow x=6$
$\therefore$ The sides of the triangle are $(3\times 6)cm,(4\times 6)cm$ and $(5\times 6)cm$ i.e $18cm,24cm$ and $30cm$
Perimeter of the $\Delta$ =$18cm+24cm+30cm$
= 72 cm