question_answer

The length of the diagonal of a square is \[7\sqrt{2}cm.\]. Then, the area of the square (in \[\text{c}{{\text{m}}^{\text{2}}}\]) is:

A) \[28\]

B) \[14\sqrt{2}\]

C) \[21\]

D) \[49\]

Correct Answer: D

Solution :

[d] Let ABCD be the square with side length x cm.

In \[\Delta ABC,\] by Pythagoras theorem,

\[A{{C}^{2}}=B{{C}^{2}}+A{{B}^{2}}\]

\[\Rightarrow \,\,\,{{(7\sqrt{2})}^{2}}={{x}^{2}}+{{x}^{2}}\] (Given, \[AC=7\sqrt{2}\,cm\])

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,49\times 2=2{{x}^{2}}\]

\[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,{{x}^{2}}=49\]

\[\therefore \]  Area of square \[={{x}^{2}}=49c{{m}^{2}}\]