The area of a field in the shape of a triangle with each side $$x$$ metres is equal to the area of another triangular field having sides 50 m, 70 m and 80 m. The value of $$x$$ is closest to:

Solution (By Examveda Team)

$$\eqalign{ & 2S = 50 + 70 + 80 \cr & S = 100 \cr & A = \sqrt {S\left( {S - a} \right)\left( {S - b} \right)\left( {S - c} \right)} \cr & A = \sqrt {100 \times 50 \times 30 \times 20} \cr & A = 1000\sqrt 3 \cr & \frac{{\sqrt 3 }}{4}{x^2} = 1000\sqrt 3 \cr & {x^2} = 4000 \cr & x = 63.2 \cr} $$