Question

The perimeter of a triangular field is 420 m and its sides are in the ratio 6:7:8. Find the area of the triangular field.

• A. $420\sqrt{15}{m}^2$
• B. $1050\sqrt{7}{m}^2$
• C. $1050\sqrt{15}{m}^2$
• D. $2100\sqrt{15}{m}^2$

Answer 1

The correct option is D $2100\sqrt{15}{m}^2$

Let the sides be 6x, 7x, 8x.
Then, $6x+7x+8x=420$
$\Rightarrow 21x=420$
$x=20$
$\therefore$ the sides are:
a =120 m, b =140 m, c =160 m
Semi-perimeter s = $\frac{420}{2}=210m$
$A=\sqrt{s(s-a)(s-b)(s-c)}$
$=\sqrt{210(210-120)(210-140)(210-160)}$
$=\sqrt{210\times 90\times 70\times 50}$
$=2100\sqrt{15}{m}^2$