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1. The breadth of a rectangular field is $\frac{3}{4}$ of its length and its area is 300 sq. metres. What will be the area (in sq. metres) of the garden of breath 1.5 metres developed around the field ?

A. 96 m²

B. 105 m²

C. 114 m²

D. Cannot be determined

Solution:

Let the length of the field be x metres
Then, breadth of the field =

\frac{3 x}{4}

metres

\begin{aligned} x \times \frac{3 x}{4} = 300 \\ \Rightarrow x^{2} = 300 \times \frac{4}{3} \\ \Rightarrow x^{2} = 400 \\ \Rightarrow x = 20 \end{aligned}

So, length = 20 m, breadth = 15 m
∴ Area of the garden :

\begin{aligned} = [{(20 + 3) \times (15 + 3)} - (20 \times 15)] m^{2} \\ = [(23 \times 18) - (20 \times 15)] m^{2} \\ = (414 - 300) m^{2} \\ = 114 m^{2} \end{aligned}

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