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 \[ABC,\] |
\[{{\text{(Hypotenuse)}}^{\text{2}}}={{\text{(Base)}}^{\text{2}}}+{{\text{(Perpendicular)}}^{\text{2}}}\] |
\[A{{C}^{2}}=A{{B}^{2}}+B{{C}^{2}}\] |
\[\Rightarrow \] \[{{(x+2)}^{2}}={{(x-2)}^{2}}+{{x}^{2}}\] |
\[\Rightarrow \]\[{{x}^{2}}+4x+4={{x}^{2}}-4x+4+{{x}^{2}}\] |
\[\Rightarrow \] \[{{x}^{2}}-8x=0\] |
\[\Rightarrow \] \[x\,\,(x-8)=0\] |
\[\Rightarrow \] \[x=8\] |
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