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. $$108{m^2}$$
Answer: Option D
Solution(By Examveda Team)
Let l and b be the length and breadth of the rectangle respectively.Then,
$$\eqalign{ & \Rightarrow \sqrt {{l^2} + {b^2}} = 15 \cr & \Rightarrow \left( {{l^2} + {b^2}} \right) = {\left( {15} \right)^2} \cr & \Rightarrow {l^2} + {b^2} = 225 \cr} $$
And,
$$\eqalign{ & \Rightarrow l + b = 3 \cr & \Rightarrow {\left( {l - b} \right)^2} = 9 \cr & \Rightarrow {l^2} + {b^2} - 2lb = 9 \cr & \Rightarrow 225 - 2lb = 9 \cr & \Rightarrow 2lb = 216 \cr & \Rightarrow lb = 108 \cr} $$
Hence, area of the field $$ = lb = 108\,{m^2}$$
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