The diagonal of a square is 10sqrt(2) cm then its perimeter is ______.

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The diagonal of a square is 10sqrt(2) cm then its perimeter is 40 cm. Explanation: In ∆ABC, $\angle$B = $90^\circ$ and $\angle$BAC = $\angle$BCA = $45^\circ$ $\therefore$ AB = 1/sqrt(2) AC ...[Theorem of $45^\circ$ – $45^\circ$ – $90^\circ$ triangle] $\therefore$ AB = 1/sqrt(2) xx 10sqrt(2) $\therefore$ AB = 10 cm $\therefore$ Perimeter of square = 4 (AB) = 4 $\times$ 10 = 40 cm.

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