The perimeter of a square is 48 inches. What would be the length, in inches, of its diagonal?
What is the length of the diagonal of a square with perimeter $48$ inches?
0
$\begingroup$
trigonometry
triangles
-
0If 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
1
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.
0
$4a=48$
$a=12$
Length of diagonal $l$, of Every square with lenght of side=$a$, is
$l=a\sqrt{2}$
$l=12\sqrt{2}\approx16.97 $
-
0You 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