Question

The sides of a triangle park are in ratio 3:5:7, if its perimeter is 90 m, Find its area.

• A. = $135m^2$
• B. = $135\sqrt{3}{m}^2$
• C. = $132\sqrt{3}{m}^2$
• D. = $138\sqrt{3}{m}^2$

Answer 1

The correct option is B

= $135\sqrt{3}{m}^2$

Let the sides be $3x,5x,7x$

Given $3x+5x+7x=90$

$\Rightarrow 15x=90$

$\Rightarrow x=6$

Therefore the sides are 18cm, 30cm and 42 cm

Semiperimeter = $\frac{90}{2}=45$

Area of triangle = $\sqrt{45(45-18)(45-30)(45-42)}$

= $\sqrt{45\times 27\times 15\times 3}$

= $\sqrt{9\times 5\times 9\times 3\times 3\times 5\times 3}$

= $9\times 5\times 3\times \sqrt{3}$

= $135\sqrt{3}{m}^2$