A) 17 cm
B) 26 cm
C) 30 cm
D) 34 cm
Correct Answer: D
Solution :
Let the length of the side of the square be x cm. \[\therefore \] \[{{x}^{2}}=(x+5)(x-3)\] \[\Rightarrow \] \[{{x}^{2}}={{x}^{2}}+5x-3x-15\] \[\Rightarrow \] \[2x=15\]\[\Rightarrow \]\[x=\frac{15}{2}\,\,cm\] Now, length of the rectangle \[=x+5=\frac{15}{2}+5=\frac{25}{2}\,\,cm\] and breadth\[=\frac{15}{2}-3=\frac{15-6}{2}=\frac{9}{2}\,\,cm\] \[\therefore \]Required perimeter \[=2\left( \frac{25}{2}+\frac{9}{2} \right)=2\times \frac{34}{2}=34\,\,cm\]
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