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:

Sides of second triangular field are 50 m, 70 m and 80 m

Half perimeter of second triangular field(s) = $$\frac{50+70+80}{2}$$ = $$\frac{200}{2}$$ = 100 m

Area of second triangular field = $$\sqrt{s\left(s-a\right)\left(s-b\right)\left(s-c\right)}$$

$$=\sqrt{100\left(100-50\right)\left(100-70\right)\left(100-80\right)}$$

$$=\sqrt{100\left(50\right)\left(30\right)\left(20\right)}$$

$$=1000\sqrt{3}$$ m$$^2$$

Given, area of both the triangular fields are equal

$$\therefore\ $$Area of first triangular field = $$1000\sqrt{3}$$ m$$^2$$

$$\Rightarrow$$  $$\frac{\sqrt{3}}{4}$$x$$^2$$ = $$1000\sqrt{3}$$

$$\Rightarrow$$  x$$^2$$ = 4000

$$\Rightarrow$$  x = $$\sqrt{4000}$$

$$\Rightarrow$$  x = 63.2 m

Hence, the correct answer is Option B