Question : The area of a square is 100 sq. cm. Find the length (in cm) of its diagonal.
Option 1: $10\sqrt{2}$
Option 2: $10$
Option 3: $20\sqrt{2}$
Option 4: $20$
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Correct Answer: $10\sqrt{2}$
Solution : The area of a square is given by the formula $A = s^2$, where $s$ is the length of a side. Given that the area is 100 sq. cm. $s = \sqrt{A} = \sqrt{100} = 10 \text{ cm}$ The length of the diagonal $d$ of a square, $d = s\sqrt{2}$ On substituting $s$ = 10 cm, $d = 10\sqrt{2} \text{ cm}$ Hence, the correct answer is $10\sqrt{2}$.
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