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# What is the perimeter of a square with area 9p^2/16 ?

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Math Expert
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What is the perimeter of a square with area 9p^2/16 ? [#permalink]

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22 Aug 2016, 01:56
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85% (00:26) correct 15% (00:38) wrong based on 59 sessions

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What is the perimeter of a square with area 9p^2/16 ?

A. 3p/4
B. 3p^2/4
C. 3p
D. 3p^2
E. 4p/3
[Reveal] Spoiler: OA

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Re: What is the perimeter of a square with area 9p^2/16 ? [#permalink]

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22 Aug 2016, 03:01
What is the perimeter of a square with area 9p^2/16 ?

Area of square, (side)^2 = (3p/4)^2

Therefore side of the square = 3p/4
Perimeter of square = 4*side = 4* (3p/4) = 3p

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Re: What is the perimeter of a square with area 9p^2/16 ? [#permalink]

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29 Nov 2017, 21:14
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Expert's post
Hi All,

We're told that the area of a SQUARE is (9P^2)/16. We're asked for the PERIMETER of the square. This question can be solved by TESTing VALUES.

Since the denominator is 16, we can 'cancel' it out if we make P=4...

IF... P=4, then the area of the square is 9(16)/16 = 9. This means that each side of the square = 3. Thus, we're looking for an answer that equals 4(3) = 12 when we plug P=4 into the answer choices. There's only one answer that matches...

[Reveal] Spoiler:
C

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What is the perimeter of a square with area 9p^2/16 ? [#permalink]

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30 Nov 2017, 05:36
Bunuel wrote:
What is the perimeter of a square with area 9p^2/16 ?

A. 3p/4
B. 3p^2/4
C. 3p
D. 3p^2
E. 4p/3

Find $$s$$.

Area of square = $$s^2 = \frac{9\pi^2}{16}$$

$$\sqrt{s^2} = \frac{(\sqrt{9})*(\sqrt{\pi^2})}{\sqrt{16}}$$

$$s= \frac{3\pi}{4}$$

Perimeter = $$4s=(\frac{3\pi}{4})*4 = 3\pi$$

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Re: What is the perimeter of a square with area 9p^2/16 ? [#permalink]

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30 Nov 2017, 06:04
Area = 9p^2/16
So a^2 = 9p^2/16 ( assumed side of a square as a)

So a = 3p/4
And perimeter of square is sum of all sides
So perimeter = 4a

So ans is 4(3p/4) = 3p

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Re: What is the perimeter of a square with area 9p^2/16 ? [#permalink]

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30 Nov 2017, 11:15
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Expert's post
Bunuel wrote:
What is the perimeter of a square with area 9p^2/16 ?

A. 3p/4
B. 3p^2/4
C. 3p
D. 3p^2
E. 4p/3

We know that the area of square = (side)^2

Thus, we can write :
$$(Side)^2 = \frac{9p^2}{16}$$

$$(Side)^2 = (\frac{3p}{4})^2$$

Since the side of square is always positive, we can conclude that the length of each side $$= \frac{3p}{4}$$

And the perimeter of the square $$= 4 * side = 4 * \frac{3p}{4} = 3p$$

The correct answer is Option C.
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Re: What is the perimeter of a square with area 9p^2/16 ? [#permalink]

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03 Dec 2017, 17:47
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Expert's post
Bunuel wrote:
What is the perimeter of a square with area 9p^2/16 ?

A. 3p/4
B. 3p^2/4
C. 3p
D. 3p^2
E. 4p/3

Since a side of the square is equal to √(9p^2/16) = 3p/4, then the perimeter of the square is 4 x 3p/4 = 12p/4 = 3p.

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Re: What is the perimeter of a square with area 9p^2/16 ?   [#permalink] 03 Dec 2017, 17:47
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