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:

Answer: Option B

Solution

Answer: Option B

Solution:

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