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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