Question

The perimeter of a triangular field is 90 m and the ratio of the sides is 3 : 5 : 7. Find the area of the field.

• A. $135m^2$
• B. $125m^2$
• C. $125\sqrt{3}{m}^2$
• D. $135\sqrt{3}{m}^2$

Answer 1

The correct option is D $135\sqrt{3}{m}^2$

Given: Perimeter of the field = 90 m
Ratio of the sides = 3 : 5 : 7

Sum of ratios:- 3 + 5 + 7 = 15

$\therefore$ First side = $\frac{3}{15}\times 90m=18m$

Second side = $\frac{5}{15}\times 90m=30m$

Third side = $\frac{7}{15}\times 90m=42m$

Now,
$s=\frac{Perimeter}{2}=\frac{90m}{2}=45m$

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

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

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

= $\sqrt{15\times 3\times 9\times 3\times 15\times 3}$

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