# What is the length of the diagonal of a square with perimeter $48$ inches? [closed]

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

• Any clues as to what maths you might know which might help you to answer this? Have you tried drawing a diagram? Mar 30 '12 at 20:55
• Can you find the length of a side of this square? Assuming you can do this, the diagonal will be the hypotenuse of a right triangle . . . Mar 30 '12 at 20:56
• 48:4=12, 12 inch. is each side of the square. Now use Pythagorean theorem to compute the diagonal. Mar 30 '12 at 20:57
• I picked this question from my GRE Book which has answer on it. But answer which i received is differing from Book Answer Mar 30 '12 at 20:59
• In a case such as you described (Medex, comment #4), what you want to do is tell how you solved the problem (and give the specific answer you got), then give the different answer from the Book Answer (and say that it's the Book Answer), and then ask if the Book Answer is wrong or if you're wrong (could be both, of course), and if you're wrong, what your mistake(s) is (are). Mar 30 '12 at 21:21

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.

$4a=48$

$a=12$

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

$l=a\sqrt{2}$

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

• Do you want to change the very last equals sign? It should be an $\approx$ sign because $12\sqrt{2}$ is not equal to 16.97... Dec 11 '14 at 14:20
• @JpMcCarthy You are right, it should be $\approx$ Dec 11 '14 at 14:23
• 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 $12\sqrt{2}=16.9705627485$. Dec 11 '14 at 14:26