Question

The sides of a triangular plot are in the ratio of 3:5:7 and its perimeter is 300 m. Find the area of the plot.

• A. $1500\sqrt{2}{m}^2$
• B. $1500\sqrt{3}{m}^2$
• C. $1425\sqrt{2}{m}^2$
• D. $1500m^2$

Answer 1

The correct option is B $1500\sqrt{3}{m}^2$

Let x be HCF. Then sides $a=3x;b=5x\&c=7x$
Perimeter, $3x+5x+7x=300\Rightarrow x=20$

Then the sides $a=60\text{m};b=100\text{m}\&c=140\text{m}$

Semiperimeter$s=\frac{60+100+140}{2}=150m$

$Area=\sqrt{s(s-a)(s-b)(s-c)}=\sqrt{150(150-60)(150-100)(150-140)}=\sqrt{150\times 90\times 50\times 10}=1500\sqrt{3}{\text{m}}^2$