A) length \[=12\text{ }m\] and breadth \[=8\text{ }m\]
B) length \[=8\text{ }m\] and breadth \[=12\text{ }m\]
C) length \[=12\text{ }m\] and breadth \[=6\text{ }m\]
D) length \[=8\text{ }m\] and breadth \[=4\text{ }m\]
Correct Answer: A
Solution :
Let the length of the garden be 'x' m. Then, breadth \[=\frac{2}{3}x\,m\] Perimeter \[=2\,(length+breadth)\] \[=2\left( x+\frac{2}{3}x \right)\] \[\therefore \] \[2x+2\left( \frac{2x}{3} \right)=40\] \[\Rightarrow \] \[2x+\frac{4x}{3}=40\] (Given : Perimeter is 40 m.) \[\Rightarrow \] \[6x+4x=120\] \[\Rightarrow \] \[10x=120\] \[\therefore \] \[x=\frac{120}{10}=12\] \[\therefore \] Length is \[12\text{ }m\] and breadth is \[\frac{2}{3}\times 12=8\,m\]
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