A) \[4\sqrt{2}\,cm\]
B) \[2\sqrt{2}\,cm\]
C) \[4\,cm\]
D) \[2\,cm\]
Correct Answer: A
Solution :
[a] Given, \[\Delta ABC\] is an isosceles triangle |
and \[\angle C=90{}^\circ \] |
\[\therefore \,\,\,\,\,\,\,\,AC=BC\] |
\[=4cm\] |
\[\Rightarrow \] AB is the longest side. |
\[\therefore \] In \[\Delta ABC,\] |
\[A{{B}^{2}}=A{{C}^{2}}+B{{C}^{2}}\] (By Pythagoras theorem) |
\[\Rightarrow \,\,\,\,\,\,\,A{{B}^{2}}={{4}^{2}}+{{4}^{2}}=16+16=32\] |
\[\Rightarrow \,\,\,\,\,\,\,AB=\sqrt{32}=\sqrt{16\times 2}=4\sqrt{2}\,cm\] |
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