question_answer

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

A)  5 cm               

B)  10 cm

C)  \[5\sqrt{2}\,\,cm\]         

D)  2.5 cm

Correct Answer: C

Solution :

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