question_answer

\[\Delta ABC\]is an isosceles triangle in which \[\angle C=90{}^\circ \]. If \[\text{BC}=\text{4cm},\]then find AB.

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)

\[\Rightarrow \,\,\,\,\,\,\,A{{B}^{2}}={{4}^{2}}+{{4}^{2}}=16+16=32\]

\[\Rightarrow \,\,\,\,\,\,\,AB=\sqrt{32}=\sqrt{16\times 2}=4\sqrt{2}\,cm\]