A) 5 cm
B) 10 cm
C) \[5\sqrt{2}\,\,cm\]
D) \[10\sqrt{2}\,\,cm\]
Correct Answer: B
Solution :
\[AB=BC=x\text{ }cm.\] \[\therefore \]\[AC=\sqrt{A{{B}^{2}}+B{{C}^{2}}}=\sqrt{{{x}^{2}}+{{x}^{2}}}=\sqrt{2{{x}^{2}}}\] \[=\sqrt{2}x\,cm.\] \[\therefore \] \[AB+BC+CA=10+10\sqrt{2}\] \[\Rightarrow \] \[2x+\sqrt{2}x=10+10\sqrt{2}\] \[\Rightarrow \] \[\sqrt{2}x\,\,\left( \sqrt{2}+1 \right)=10\left( 1+\sqrt{2} \right)\] \[\Rightarrow \] \[\sqrt{2}x=10\,cm.=AC\]You need to login to perform this action.
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