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Express the area A of a square as a function of its perimeter. The answer is A=p^2/16?

I tried everything i could think of, please help me! Tell me how you did it.
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Dana Herzog

Feb 20, 2025

If s is the length of the side of the square, then the perimeter (P) is equal to 4*s, so we have:P = 4sSolve this for s, givings = P / 4Now the area of a square (A) is equal to the length of the side squares, s^2.A = s^2Put in s from what we found above, to get:A = (P / 4)^2You can square a fraction by squaring the top and bottom separately, so this becomes:A = P^2 / 4^2= P^2 / 16... Show More
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D
Dana Herzog

Feb 20, 2025

The area of any rectangle can be found by multiplying length by height. Since length and height are the same in a square, the area of a square is equal to any side multiplied by itself.The perimeter of a square is four times any side, so A = (p/4)^2When squaring a fraction, you can square the numerator and denominator separately:A = p^2 / 4^2 = p^2/16... Show More
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