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

Question

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

PKN · Answer

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)

sudarshan22 · Answer

+1 for   D  .

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

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

Hence,   D  .

KSBGC · Answer

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.

Abhishek009 · Answer

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)

ScottTargetTestPrep · Answer

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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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

Prep Toolkit

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