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The perimeter of a square is 48 inches. What would be the length, in inches, of its diagonal?

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    If the perimeter is 48, it's not hard to find the lengths of the sides. Then use the Pythagorean theorem.2012-03-30

2 Answers 2

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Since the perimeter of the square is 48 inches, each side is 12 inches. Using the Pythagorean theorem ($a^{2}$ + $b^{2}$ = $c^{2}$), we have $12^{2}+12^{2} = diagonal^{2}$ $288 = diagonal ^{2}$

Thus, the diagonal is about $16.97$ inches.

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$4a=48$

$a=12$

Length of diagonal $l$, of Every square with lenght of side=$a$, is

$l=a\sqrt{2}$

$l=12\sqrt{2}\approx16.97 $

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    You can write $12\sqrt{2}\approx 16.97$ or $12\sqrt{2}\approx 16.9705627485\approx 16.97$ or maybe $12\sqrt{2}=16.9705...\approx 16.97$. It is incorrect to write $12\sqrt{2}=16.9705627485$.2014-12-11