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If a rectangle of area 24 can be partitioned into exactly 3
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15 Jun 2020, 01:21
15 Jun 2020, 01:21
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If a rectangle of area 24 can be partitioned into exactly 3 nonoverlapping squares of equal area, what is the length of the longest side of the rectangle?
A. \(2\sqrt{2}\)
B. 6
C. 8
D. \(6\sqrt{2}\)
E. \(12\sqrt{2}\)
A. \(2\sqrt{2}\)
B. 6
C. 8
D. \(6\sqrt{2}\)
E. \(12\sqrt{2}\)
Re: If a rectangle of area 24 can be partitioned into exactly 3
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15 Jun 2020, 01:22
15 Jun 2020, 01:22
Expert Reply
Post A Detailed Correct Solution For The Above Questions And Get A Kudos.
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
Question From Our New Project: GRE Quant Challenge Questions Daily - NEW EDITION!
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Re: If a rectangle of area 24 can be partitioned into exactly 3
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15 Jun 2020, 05:54
15 Jun 2020, 05:54
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Carcass wrote:
If a rectangle of area 24 can be partitioned into exactly 3 nonoverlapping squares of equal area, what is the length of the longest side of the rectangle?
A. \(2\sqrt{2}\)
B. 6
C. 8
D. \(6\sqrt{2}\)
E. \(12\sqrt{2}\)
A. \(2\sqrt{2}\)
B. 6
C. 8
D. \(6\sqrt{2}\)
E. \(12\sqrt{2}\)
Let's work backwards
Here are 3 squares (with sides length x) comprising a rectangle
So, the rectangle has base of 3x and height of x
GIVEN: The rectangle has area 24
Area of rectangle = (base)(height)
We can write: 24 = (3x)(x)
Simplify: 24 = 3x²
So 8 = x²
This means x = √8 = √[(4)(2)] = (√4)(√2) = 2√2
What is the length of the longest side of the rectangle?
The longest side had length 3x
3x = 3(2√2) = 6√2
Answer: D
Cheers,
Brent
