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# A square region has an area of b square inches and a perimeter of n in

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Math Expert
Joined: 02 Sep 2009
Posts: 58445
A square region has an area of b square inches and a perimeter of n in  [#permalink]

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31 Oct 2018, 02:06
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Difficulty:

15% (low)

Question Stats:

81% (01:24) correct 19% (02:07) wrong based on 33 sessions

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A square region has an area of b square inches and a perimeter of n inches. If n = b/3 what is the length, in inches, of the side of the square?

A. 12
B. 12√2
C. 48
D. 48√2
E. 144

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Re: A square region has an area of b square inches and a perimeter of n in  [#permalink]

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31 Oct 2018, 02:16
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Let the side of a square be 'a'. Given the area of square $$a^2 = b$$

Now perimeter of the square is $$4a = n$$

Given, $$n = \frac{b}{3}$$

$$4a = \frac{a^2}{3}$$

$$a = 12$$

OPTION : A
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A square region has an area of b square inches and a perimeter of n in  [#permalink]

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Updated on: 31 Oct 2018, 03:01
1
side of square = $$\sqrt{b}$$

Perimeter of a square = 4*side = 4 * $$\sqrt{b}$$

Given the perimeter = n

then 4*$$\sqrt{b}$$ = $$\frac{b}{3}$$

then it becomes $$12 = \frac{b}{\sqrt{b}}$$

squaring both sides we get $$144 = \frac{b^2}{b}$$

this then equals 144 = b

b = 144 is the area

Taking the square root of 144 = 12

Side is then 12.

Thanks to eswarchethu135 for pointing out

Originally posted by Salsanousi on 31 Oct 2018, 02:21.
Last edited by Salsanousi on 31 Oct 2018, 03:01, edited 1 time in total.
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Re: A square region has an area of b square inches and a perimeter of n in  [#permalink]

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31 Oct 2018, 02:24
hi eswarchethu135

I think you started off with the wrong equation $$a^2 =$$b it should be $$area = b$$

so it means area = $$\sqrt{b} * \sqrt{b}$$ = b
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Re: A square region has an area of b square inches and a perimeter of n in  [#permalink]

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31 Oct 2018, 02:39
Hi Salsanousi

I took the side of a square as 'a', then the area will be $$a^2$$. Now the area is equal to 'b'. So $$a^2 = b$$. Question said the area of a square is 'b'. However, I don't find any mistake in your approach too. Will wait for OA
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Re: A square region has an area of b square inches and a perimeter of n in  [#permalink]

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31 Oct 2018, 02:58
Hi eswarchethu135 You're right! what I found was actually the area not the side ^_^

So I should take the square root of b to find the side.

Thank you!
Re: A square region has an area of b square inches and a perimeter of n in   [#permalink] 31 Oct 2018, 02:58
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