SSC Sample Paper Mock Test-5 SSC CGL Tear-II Paper-1

The side of a square exceeds the side of the another square by 4 cm and the sum of the areas of the two squares is \[400\,\,c{{m}^{2}}.\] The dimensions of the squares is

A) 8 cm and 12 cm

B) 6 cm and 10 cm

C) 12 cm and 16 cm

D) None of these

Correct Answer: C

Solution :

Let side of a square = x cm

Side of another square = (x + 4) cm

\[\Rightarrow \] \[{{x}^{2}}+{{(x+4)}^{2}}=400\] (by condition)

\[{{x}^{2}}+{{x}^{2}}+16+8x=400\]

\[\Rightarrow \] \[2{{x}^{2}}+8x-384=0\]

\[{{x}^{2}}+4x-192=0\]\[\Rightarrow \]\[(x-12)(x+16)=0\]

\[\Rightarrow \]\[x-12=0\]or\[x+16=0\]

\[x=12\] or \[x=-16\](not possible)

So, side of one square =12 can

Side of another square \[=\text{ }12+4=16\text{ cm}\]