Question

The length of the diagonal of square is 20 CM find its area

Answer 1

Let the side be x,

$by \: pythagorean \: theorum\\ \\ {side}^{2} + {side}^{2} = {diagonal}^{2} \\ \\ {x}^{2} + {x}^{2} = 400 \\ \\ 2 {x}^{2} = 400 \\ \\ {x }^{2} = \frac{400}{2} \\ \\ {x}^{2} = 200 \\ \\ x = \sqrt{200} \\ \\ so \: side \: of \: square \: is \: \sqrt{200} cm. \: \\ area \: of \: square = side \times side \\ area \: of \: square \: = {{( \sqrt{200} cm)}}^{2} \: \\ area = 200 {cm}^{2}$

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