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1. The diagonal of a rectangular field is 15 metres and the difference between its length its length and width is 3 metres. The area of the rectangular field is :

A. $9 m^{2}$

B. $12 m^{2}$

C. $21 m^{2}$

D. $108 m^{2}$

Solution:

Let l and b be the length and breadth of the rectangle respectively.
Then,

\begin{aligned} \Rightarrow \sqrt{l^{2} + b^{2}} = 15 \\ \Rightarrow (l^{2} + b^{2}) = {(15)}^{2} \\ \Rightarrow l^{2} + b^{2} = 225 \end{aligned}

And,

\begin{aligned} \Rightarrow l + b = 3 \\ \Rightarrow {(l - b)}^{2} = 9 \\ \Rightarrow l^{2} + b^{2} - 2 l b = 9 \\ \Rightarrow 225 - 2 l b = 9 \\ \Rightarrow 2 l b = 216 \\ \Rightarrow l b = 108 \end{aligned}

Hence, area of the field

= l b = 108 m^{2}

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