If the diagonal and the area of a rectangle are 25 m2 and 168 m2, what is the length of the rectangle ?

Answer: Option C

Let the length of the rectangle be x metres.
Then, breath of the rectangle = $$\left(\frac{168}{x}\right)m$$
$$\begin{array}{rl}& \therefore \sqrt{x^2+{\left(\frac{168}{x}\right)}^2}=25\\ & \Rightarrow \sqrt{x^2+\frac{28224}{x^2}}=25\\ & \Rightarrow x^2+\frac{28224}{x^2}=625\\ & \Rightarrow x^4-625x^2+28224=0\\ & \Rightarrow x^4-576x^2-49x^2+28224=0\\ & \Rightarrow x^2\left(x^2-576\right)-49\left(x^2-576\right)=0\\ & \Rightarrow \left(x^2-576\right)\left(x^2-49\right)=0\\ & \Rightarrow x^2=576or{x}^2=49\\ & \Rightarrow x=24orx=7\end{array}$$
Hence, length = 24 m and breadth = 7 m