ABC26GN4336 · Area
Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
If the diagonal and the area of a rectangle are 25 m and $168 \mathrm{m}^{2}$, what is the length of the rectangle?
(a)12 m
(b)17 m
(c)24 m
(d)31 m
Answer
Explanation
Let the length of the rectangle be $x$ metres. Then, breadth of the rectangle $=\left(\frac{168}{x}\right) \mathrm{m}$. $$\begin{aligned} \therefore \sqrt{x^{2}+\left(\frac{168}{x}\right)^{2}}=25 & \Rightarrow \sqrt{x^{2}+\frac{28224}{x^{2}}}=25 \\ & \Rightarrow x^{2}+\frac{28224}{x^{2}}=625 \end{aligned} \begin{aligned} & \Rightarrow x^{4}-625 x^{2}+28224=0 \\ & \Rightarrow x^{4}-576 x^{2}-49 x^{2}+28224=0 \\ & \Rightarrow x^{2}\left(x^{2}-576\right)-49\left(x^{2}-576\right)=0 \\ & \Rightarrow\left(x^{2}-576\right)\left(x^{2}-49\right)=0 \\ & \Rightarrow x^{2}=576 \text { or } x^{2}=49 \Rightarrow x=24 \text { or } x=7 \end{aligned}$$ Hence, length $=24 \mathrm{m}$ and breadth $=7 \mathrm{m}$.
Open in whiteboard · Browse this chapter in the app