Question

A lawn is in the form of a rectangle whose sides are in the ratio 5 : 3 and its area is 3375 m². Find the cost of fencing the lawn at Rs 20 per metre.

Answer 1

Let the length and breadth of the lawn be $5x\mathrm{m}\mathrm{and}3x\mathrm{m}$, respectively.

Now,

Area of the lawn$=5x\times 3x=5x^{\mathit{2}}$
$$\begin{gathered} \Rightarrow 15x^2=3375 \\ \Rightarrow x=\sqrt{\frac{3375}{15}} \\ \Rightarrow x=\sqrt{225}=15 \end{gathered}$$

$$\begin{gathered} \mathrm{Length}=5x=5\times 15=75\mathrm{m} \\ \mathrm{Breadth}=3x=3\times 15=45\mathrm{m} \end{gathered}$$

∴ Perimeter of the lawn$=2\left(\mathrm{Length}+\mathrm{Breadth}\right)=2\left(75+45\right)=2\times 120=240\mathrm{m}$
Total cost of fencing the lawn at Rs 20 per metre $=240\times 20=\mathrm{Rs}4800$