A) a
B) \[a\sqrt{2}\]
C) \[\frac{a}{\sqrt{2}}\]
D) \[\frac{a}{2}\]
Correct Answer: A
Solution :
Let side of the square \[ABCD=\text{ }x\text{ }cm,\]and side of the square \[EFGH=y\text{ }cms\] In right-angle triangle OAE, \[O{{A}^{2}}=O{{E}^{2}}+E{{A}^{2}}\] or \[{{a}^{2}}={{\left( \frac{x}{2} \right)}^{2}}+{{\left( \frac{x}{2} \right)}^{2}}=\frac{{{x}^{2}}+{{x}^{2}}}{4}\] or \[2{{a}^{2}}={{x}^{2}}\] In right-angle triangle EHG, \[E{{G}^{2}}=E{{H}^{2}}+H{{G}^{2}}\] or \[{{x}^{2}}={{y}^{2}}+{{y}^{2}}\] or \[2{{y}^{2}}={{x}^{2}}=2{{a}^{2}}\] \[\therefore \] \[y=a=EF\]You need to login to perform this action.
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