Subject: General Aptitude · Chapter: Area · Exam: · Marks: · Difficulty:
The diagonal of a rectangular field is $15 m$ and its area is $108 \mathrm{sq} . m$. What will be the total expenditure in fencing the field at the rate of ₹ 5 per metre?
Answer
Answer (as printed):
Explanation
Let the length and breadth of the rectangle be $l$ and $b$ metres respectively. Then, $\sqrt{l^{2}+b^{2}}=15$ and $l b=108 \Rightarrow l^{2}+b^{2}=225$ and $l b=108$ $$\begin{aligned} & \Rightarrow(l+b)^{2}=\left(l^{2}+b^{2}\right)+2 l b=225+216=441 \\ & \Rightarrow l+b=\sqrt{441}=21 . \end{aligned}$$ ∴ Perimeter of the field $=2(l+b)=(2 \times 21) \mathrm{m}=42 \mathrm{m}$. Hence, cost of fencing $=₹(42 \times 5)=₹ 210$.