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Find the side and perimeter of a square whose diagonal is 10 cm ?

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#### Solution

It is given that ABCD is a square.

∴ AB = BC = CD = DA = *a* (say)

According to Pythagoras theorem, in ∆ABD

\[{AB}^2 + {AD}^2 = {BD}^2 \]

\[ \Rightarrow a^2 + a^2 = {10}^2 \]

\[ \Rightarrow 2 a^2 = 100\]

\[ \Rightarrow a^2 = 50\]

\[ \Rightarrow a = \sqrt{50}\]

\[ \Rightarrow a = 5\sqrt{2} cm\]

Hence, the side of the square is 5\[\sqrt{2}\] cm.

Perimeter of a square = \[4 \times \left( side \right)\]

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