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If the diagonal of a square measures 8 \ cm , what is the perimeter of the square?

(A) 16\sqrt{2} \ cm

(B) 18\sqrt{2} \ cm

(C) 32\sqrt{2} \ cm

(D) 64\sqrt{2} \ cm

Thanks

kadence

10-25-2013, 06:50 PM

Two consecutive sides of a square are perpendicular to each other and form a right angled triangle with the diagonal.

From the Pythagoras’ theorem

a^2+a^2=d^2 \Rightarrow 2a^2=d^2 \Rightarrow a^2=\frac{8^2}{2}=32

\Rightarrow a=\sqrt{32}=4\sqrt{2}

Therefore, the perimeter P is equal to 4 \cdt 4\sqrt{2} =16\sqrt{2}

Thus, the correct answer is (A).

Hope these help!!

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