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nightblade354
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Expert reply
19 Oct 2017, 09:23
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D
Be sure to select an answer first to save it in the Error Log before revealing the correct answer (OA)!
Difficulty:
5%
(low)
Question Stats:
83% (00:34) correct
17%
(00:32)
wrong
based on 104
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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) \(x^2 + 4\)
(A) \(x^2\)
(B) \(2x^2\)
(C) 4x
(D) \(4x^2\)
(E) \(x^2 + 4\)
19 Oct 2017, 09:59
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nightblade354
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) \(x^2 + 4\)
(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)²
= (2x)(2x)
= 4x²
Answer:
Cheers,
Brent
nightblade354
Current Student
Joined: 31 Jul 2017
Last visit: 11 Dec 2024
Posts: 1,751
Own Kudos:
Given Kudos: 3,185
Status:He came. He saw. He conquered. -- Going to Business School -- Corruptus in Extremis
Location: United States (MA)
Concentration: Finance, Economics
Schools: Darden '25 (M)
Expert reply
19 Oct 2017, 15:49
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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.
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.
