question_answer

The length of the three sides of a right angled triangle are \[(x-2)\,\,cm,\] \[x\] and \[(x+2)\,\,cm,\] respectively. Then, the value of \[x\]is                                                                                                 [SSC (CGL) 2012]

A) 10                                

B) 8  

C) 4                                 

D) 0

Correct Answer: B

Solution :

In a right angled \[\Delta ABC,\]

By Pythagoras theorem \[ABC,\]

\[{{\text{(Hypotenuse)}}^{\text{2}}}={{\text{(Base)}}^{\text{2}}}+{{\text{(Perpendicular)}}^{\text{2}}}\]

\[A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}}\]

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

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

\[\Rightarrow \]   \[{{x}^{2}}-8x=0\]

\[\Rightarrow \]   \[x\,\,(x-8)=0\]

\[\Rightarrow \]               \[x=8\]