Question

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

• A. $2100$ sq m
• B. $2100\sqrt{15}$ sq m
• C. $2000$ sq m
• D. $2000\sqrt{15}$ sq m

Answer 1

Answer: (B)

$2100\sqrt{15}$ sq m

Let sides of $△$ are$=6x,7x$ and $8x$

Perimeter$=6x+7x+8x=21x$

$21x=410$

$x=20$

Sides are $120,140$ and $160m$

Area $=\sqrt{S(S-A)(S-B)(S-C)}$ [Heron's Formula]

$S=\frac{120+140+160}{2}=210m$

$A=\sqrt{210(210-120)(210-140)(210-160)}$

$=2100\sqrt{15}$ sq. m