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The area of a square is A = s^2, where s is the length of one of the

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Bunuel
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The area of a square is A = s^2, where s is the length of one of the [#permalink] New post   09 Dec 2021, 02:30
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The area of a square is A = s^2, where s is the length of one of the four equal sides. If the area of a square is quadrupled, by what factor has the length of any one of the sides been changed?

(A) \(\sqrt{2}\)

(B) \(2\)

(C) \(2\sqrt{2}\)

(D) \(4\)

(E) \(\sqrt{6}\)



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Re: The area of a square is A = s^2, where s is the length of one of the [#permalink] New post   09 Dec 2021, 04:21
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The area of a square is A = \(s^2\), where s is the length of one of the four equal sides. If the area of a square is quadrupled, by what factor has the length of any one of the sides been changed?

\(A = s^2\)

If the area of a square is quadrupled, new area ,A2 = \(4 * s^2\)
Let us assume that new side be s2.

\(4 * s^2 = (s2) ^2\)

s2 = \(\sqrt{4 * s^2} \)= 2s

So the side of the square should multiplied by 2.

Option B is the answer.

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Re: The area of a square is A = s^2, where s is the length of one of the [#permalink] New post   09 Dec 2021, 04:24
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Bunuel wrote:
The area of a square is A = s^2, where s is the length of one of the four equal sides. If the area of a square is quadrupled, by what factor has the length of any one of the sides been changed?

(A) \(\sqrt{2}\)

(B) \(2\)

(C) \(2\sqrt{2}\)

(D) \(4\)

(E) \(\sqrt{6}\)



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A = S^2
A becomes 4A which is possible when S becomes 2S.

So the side of the square has been increased 100% or by a factor of 2. (B)
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Re: The area of a square is A = s^2, where s is the length of one of the [#permalink] New post   09 Dec 2021, 06:37
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Bunuel wrote:
The area of a square is A = s^2, where s is the length of one of the four equal sides. If the area of a square is quadrupled, by what factor has the length of any one of the sides been changed?

(A) \(\sqrt{2}\)

(B) \(2\)

(C) \(2\sqrt{2}\)

(D) \(4\)

(E) \(\sqrt{6}\)



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All the solutions look great, but I have a quick solution that will give the answer in seconds.
Let the initial Area (A) = 1 hence s=1
Now the New area is quadrupled so New Area = 4; so the New length of the side would be 2
And that's your solution OPTION B by simple substitution. Cheers :)
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Re: The area of a square is A = s^2, where s is the length of one of the [#permalink] New post   30 Dec 2021, 05:04
A = s^2
so, s = √A

Given, A = 4A
∴ s = √4A = 2√A (B)
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Re: The area of a square is A = s^2, where s is the length of one of the [#permalink]
30 Dec 2021, 05:04
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