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 ?
Options:
A . 96 m2
B . 105 m2
C . 114 m2
D . Cannot be determined
E . None of these
Answer: Option C Let the length of the field be x metres Then, breadth of the field = $$\frac{3x}{4}$$ metres $$\eqalign{ & x \times \frac{{3x}}{4} = 300 \cr & \Rightarrow {x^2} = 300 \times \frac{4}{3} \cr & \Rightarrow {x^2} = 400 \cr & \Rightarrow x = 20 \cr} $$ So, length = 20 m, breadth = 15 m ∴ Area of the garden : $$\eqalign{ & = \left[ {\left\{ {\left( {20 + 3} \right) \times \left( {15 + 3} \right)} \right\} - \left( {20 \times 15} \right)} \right]{m^2} \cr & = \left[ {\left( {23 \times 18} \right) - \left( {20 \times 15} \right)} \right]{m^2} \cr & = \left( {414 - 300} \right){m^2} \cr & = 114\,{m^2} \cr} $$
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