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Which of the following expresses the area of a square region in terms
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16 Jul 2018, 21:14
16 Jul 2018, 21:14
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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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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
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16 Jul 2018, 22:23
16 Jul 2018, 22:23
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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. \((\frac{4p}{p})^2\)
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]
16 Jul 2018, 23:48
16 Jul 2018, 23:48
+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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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]
17 Jul 2018, 04:26
17 Jul 2018, 04:26
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. \((\frac{4p}{p})^2\)
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]
17 Jul 2018, 07:01
17 Jul 2018, 07:01
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. \((\frac{4p}{p})^2\)
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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Abhishek....
PLEASE FOLLOW THE RULES FOR POSTING IN QA AND VA FORUM AND USE SEARCH FUNCTION BEFORE POSTING NEW QUESTIONS
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Re: Which of the following expresses the area of a square region in terms
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19 Jul 2018, 17:16
19 Jul 2018, 17:16
Expert Reply
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. \((\frac{4p}{p})^2\)
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
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19 Dec 2023, 01:54
19 Dec 2023, 01:54
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Re: Which of the following expresses the area of a square region in terms [#permalink]
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