question_answer

If \[\Delta ABC\]is an isosceles triangle with \[\angle C={{90}^{o}}\] and \[AC=5\text{ }cm,\]then AB is:

A)  \[5\,cm\]                      

B)  \[10\,cm\]        

C)         \[5\sqrt{2}\,cm\]           

D)       \[2.5\text{ }cm\]

Correct Answer: C

Solution :

\[\Delta ABC\] is an isocoles triangle.       Therefore,\[AC=BC=5\text{ }cm\]   Now,   \[A{{B}^{2}}=A{{C}^{2}}+B{{C}^{2}}\] \[A{{B}^{2}}={{5}^{2}}+{{5}^{2}}\Rightarrow \sqrt{25+25}=5\sqrt{2}\,cm\]