A) 40 cm and 52 cm
B) 50 cm and 62 cm
C) 60 cm and 72 cm
D) 70 cm and 82 cm
Correct Answer: C
Solution :
Let the sides of the two squares be x and x - 3 cm. Then, \[\Rightarrow \,\,{{x}^{2}}+{{\left( x+3 \right)}^{2}}=549\] \[\Rightarrow \]\[2{{x}^{2}}+6x+9-549=0\] \[\Rightarrow \]\[{{x}^{2}}+3x-270=0\] \[\Rightarrow \]\[{{x}^{2}}+18x-15x-270=0\] \[\Rightarrow \]\[\left( x+18 \right)\left( x-15 \right)=0\Rightarrow x=15\,\,cm\] \[\therefore \] Perimeter of the two squares are 4x cm and \[4\left( x+3 \right)cm.\] \[4\times ~15cm\]and \[4\left( 15+3 \right)cm\] = 60 cm and 72 cm
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