SSC Sample Paper Mock Test-12 SSC CGL Tear-II Paper-1

The difference of the areas of two squares drawn on two line segments of different lengths is 32 sq cm. Find the length of the greater line segment if one is longer than the other by 2 cm

A) 7 cm

B) 9 cm

C) 11 cm

D) 16 cm

Correct Answer: B

Solution :

Let the length of the smaller line segment\[=x\,\,\text{cm}\]

\[\therefore \]The length of larger line segment \[=(x+2)\,\,\text{cm}\]

According to the question,

\[{{(x+2)}^{2}}-{{x}^{2}}=32\]

\[\Rightarrow \]\[{{x}^{2}}4x+4-{{x}^{2}}=32\]

\[\Rightarrow \] \[4x=32-4=28\]

\[\Rightarrow \] \[x=\frac{28}{4}=7\]

\[\therefore \] The required length\[=x+2=7+2=9\,\,\text{cm}\]