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A certain square has sides of length x. If the length of each side is

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A certain square has sides of length x. If the length of each side is [#permalink]

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New post 19 Oct 2017, 08:23
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A certain square has sides of length x. If the length of each side is doubled, then which of the following represents the area of the resulting square, in terms of x?

(A) \(x^2\)
(B) \(2x^2\)
(C) 4x
(D) \(4x^2\)
(E) \(x^2 + 4\)
[Reveal] Spoiler: OA

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Re: A certain square has sides of length x. If the length of each side is [#permalink]

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New post 19 Oct 2017, 08:59
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nightblade354 wrote:
A certain square has sides of length x. If the length of each side is doubled, then which of the following represents the area of the resulting square, in terms of x?

(A) \(x^2\)
(B) \(2x^2\)
(C) 4x
(D) \(4x^2\)
(E) \(x^2 + 4\)


Doubling the length of each side means that each side now has length 2x
So, area of square = (side)²
= (2x
= (2x)(2x)
= 4x²

Answer:
[Reveal] Spoiler:
D


Cheers,
Brent
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Re: A certain square has sides of length x. If the length of each side is [#permalink]

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New post 19 Oct 2017, 14:49
Here is the OE from MGMAT:

We can solve this problem either by assigning a value to x or by working out the algebra. Let's try assigning a value first.

Let's say the square has sides of length 2. Therefore, x = 2. If we double the length, then the square will have sides of length 4. The area of this larger square will be 42 = 16. So we need to plug 2 (which is our assigned value of x) into the answer choices to see which one yields 16:

(A) (2)2 = 4 Incorrect
(B) 2(22) = 2(4) = 8 Incorrect
(C) 4(2) = 8 Incorrect
(D) 4(22) = 4(4) = 16 CORRECT
(E) 22 + 4 = 4 + 4 = 8 Incorrect

Alternatively, we can use algebra. If x is the length of a side and we double it, we get 2x. A square with sides of length 2x will have an area of (2x)2 = 4x2.

The correct answer is D.
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Re: A certain square has sides of length x. If the length of each side is   [#permalink] 19 Oct 2017, 14:49
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