Question

The perimeter of a triangular field is 144 m and the ratio of the sides is 3 : 4 : 5 The area of the field is

• A. $864m^2$
• B. $468m^2$
• C. $824m^2$
• D. none

Answer 1

The correct option is A $864m^2$

Let the side of the triangle $a,b$ and $c$ be $3x,4x,5x$

Perimeter $=144$ m

$\therefore 3x+4x+5x=144$

$\Rightarrow 12x=144$

$\Rightarrow x=12$

Then$a=12\times 3=36m$

$b=4\times 12=48m$

$c=5\times 12=60$

Then $s=\frac{a+b+c}{2}=\frac{36+48+60}{2}=\frac{144}{2}=72$

$\therefore$ Area of the triangle$=\sqrt{s(s-a)(s-b)(s-c)}$

$\Rightarrow \sqrt{72(72-36)(72-48)(72-60)}$

$\Rightarrow \sqrt{72\times 36\times 24\times 12}=864m^2$