Find the perimeter of a square if its diagonal is 10sqrt2 cm:

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KollegeApply · Accepted Answer

40 cm Explanation: It is given that ABCD is a square. $\therefore$ AB = BC = CD = DA = x (say) According to Pythagoras theorem, in ∆ABD AB2 + AD2 = BD2 $\Rightarrow$ x^2 + x^2 = (10sqrt2)^2 $\Rightarrow$ 2x2 = 200 $\Rightarrow$ x2 = 100 $\Rightarrow$ x = sqrt100 x = 10 cm Hence, the side of the square is 10 cm. Now, Perimeter of a square = 4 $\times$ side = 4 $\times$ x = 4 $\times$ 10 = 40 Hence, the correct option is 40 cm.

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