Question

A lawn is in the form of a rectangle whose sides are in the ratio 5 : 3. The area of the lawn is 3375 m². Find the cost of fencing the lawn at Rs 8.50 per metre.

Answer 1

Let the length and breadth of the rectangular lawn be 5x m and 3x m, respectively.

Given:
Area of the rectangular lawn = $3375{\mathrm{m}}^2$

$$\begin{gathered} \Rightarrow 3375=5x\times 3x \\ \Rightarrow 3375=15x^2 \\ \Rightarrow \frac{3375}{15}=x^2 \\ \Rightarrow 225=x^2 \\ \Rightarrow x=15 \end{gathered}$$

Thus, we have:

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


$$\begin{gathered} \mathrm{Perimeter}\mathrm{of}\mathrm{the}\mathrm{rectangular}\mathrm{lawn}=2(l+b) \\ =2(75+45) \\ =2\left(120\right) \\ =240\mathrm{m} \end{gathered}$$

Cost of fencing 1 m lawn = Rs 8.50
∴ Cost of fencing 240 m lawn = $240\times 8.50=\mathrm{Rs}2040$