A) 5 times
B) 2 times
C) 3 times
D) 4 times
Correct Answer: D
Solution :
Perimeter of smaller square with side \[{{a}_{1}}=12cm\] \[\Rightarrow \] \[4{{a}_{1}}=12\] \[\Rightarrow \] \[{{a}_{1}}=3\] Area of smaller square \[={{\left( {{a}_{1}} \right)}^{2}}={{\left( 3 \right)}^{2}}=9c{{m}^{2}}\] Perimeter of bigger square with side \[{{a}_{2}}=24\] cm \[\Rightarrow \] \[4{{a}_{2}}=24\] \[\Rightarrow \] \[{{a}_{2}}=6cm\] Area of bigger square =\[{{\left( {{a}_{2}} \right)}^{2}}=\left( {{6}^{2}} \right)=36c{{m}^{2}}.\] The area of bigger square is 4 times that of smaller square.
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