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Which of the following expresses the area of a square region in terms

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Which of the following expresses the area of a square region in terms  [#permalink]

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New post 16 Jul 2018, 20:14
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Question Stats:

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Which of the following expresses the area of a square region in terms of its perimeter, p ?


A. \(\frac{p}{4}\)

B. \(\frac{p^2}{4}\)

C. \(\frac{p}{16}\)

D. \(\frac{p^2}{16}\)

E. \((\frac{4p}{p})^2\)

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Re: Which of the following expresses the area of a square region in terms  [#permalink]

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New post 16 Jul 2018, 21:23
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Bunuel wrote:
Which of the following expresses the area of a square region in terms of its perimeter, p ?


A. \(\frac{p}{4}\)

B. \(\frac{p^2}{4}\)

C. \(\frac{p}{16}\)

D. \(\frac{p^2}{16}\)

E. \((\frac{4p}{p})^2\)


Perimeter of square=p=4a Or, \(a=\frac{p}{4}\)
Area of square with side 'a'=\(a^2=(\frac{p}{4})^2\)=\(\frac{p^2}{16}\)

Ans. (D)
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Re: Which of the following expresses the area of a square region in terms  [#permalink]

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New post 16 Jul 2018, 22:48
+1 for D.

Perimeter -> p = 4x
x = p / 4

Therefore,
Area = x^2 = ( p / 4 )^2 = p^2 / 16

Hence, D.
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Which of the following expresses the area of a square region in terms  [#permalink]

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New post 17 Jul 2018, 03:26
Bunuel wrote:
Which of the following expresses the area of a square region in terms of its perimeter, p ?


A. \(\frac{p}{4}\)

B. \(\frac{p^2}{4}\)

C. \(\frac{p}{16}\)

D. \(\frac{p^2}{16}\)

E. \((\frac{4p}{p})^2\)



Area of a square region = \((one of the legs of square )^2\)

Here the perimeter id given. Thus we need to divide the perimeter by 4.

Area of the square =\((p/4)^2\) = \(p^2\) / 16

Thus the best answer is D.
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Re: Which of the following expresses the area of a square region in terms  [#permalink]

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New post 17 Jul 2018, 06:01
Bunuel wrote:
Which of the following expresses the area of a square region in terms of its perimeter, p ?


A. \(\frac{p}{4}\)

B. \(\frac{p^2}{4}\)

C. \(\frac{p}{16}\)

D. \(\frac{p^2}{16}\)

E. \((\frac{4p}{p})^2\)


Area \((A)\) of a square in terms of Perimeter \((p)\) will always be \((\frac{p}{4})^2\) = \(\frac{p^2}{16}\) , Answer must be (D)
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Re: Which of the following expresses the area of a square region in terms  [#permalink]

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New post 19 Jul 2018, 16:16
Bunuel wrote:
Which of the following expresses the area of a square region in terms of its perimeter, p ?


A. \(\frac{p}{4}\)

B. \(\frac{p^2}{4}\)

C. \(\frac{p}{16}\)

D. \(\frac{p^2}{16}\)

E. \((\frac{4p}{p})^2\)


We can create the equations:

p = 4s (where s = side)

p/4 = s

and

A = s^2

Substituting, we have:

A = (p/4)^2 = p^2/16

Alternate Solution:

The perimeter of the square is p, so one side of the square is p/4. We know that the area of a square is (side)^2 = (p/4)^2 = p^2/16.

Answer: D
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Re: Which of the following expresses the area of a square region in terms &nbs [#permalink] 19 Jul 2018, 16:16
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