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

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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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New post 31 Oct 2018, 01:06
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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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New post 31 Oct 2018, 01:16
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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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New post Updated on: 31 Oct 2018, 02:01
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

Answer choice E

b = 144 is the area

Taking the square root of 144 = 12

Side is then 12.

Thanks to eswarchethu135 for pointing out :grin:

Correct answer choice is A

Originally posted by Salsanousi on 31 Oct 2018, 01:21.
Last edited by Salsanousi on 31 Oct 2018, 02:01, 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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New post 31 Oct 2018, 01:24
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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New post 31 Oct 2018, 01:39
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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New post 31 Oct 2018, 01:58
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!
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Re: A square region has an area of b square inches and a perimeter of n in &nbs [#permalink] 31 Oct 2018, 01:58
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