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If a rectangle of area 24 can be partitioned into exactly 3 nonoverlap

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Bunuel
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If a rectangle of area 24 can be partitioned into exactly 3 nonoverlap [#permalink] New post  26 Apr 2019, 06:20
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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. \(12\sqrt{2}\)


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BrentGMATPrepNow
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Re: If a rectangle of area 24 can be partitioned into exactly 3 nonoverlap [#permalink] New post  26 Apr 2019, 08:21
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Bunuel 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. \(12\sqrt{2}\)


PS88502.01
Quantitative Review 2020 NEW QUESTION


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

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Brent
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Re: If a rectangle of area 24 can be partitioned into exactly 3 nonoverlap [#permalink] New post  23 May 2019, 04:54
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Solution


Given
In this question, we are given
    • A rectangle of area 24 is partitioned into exactly 3 nonoverlapping squares of equal area.

To Find
We need to determine
    • The length of the longest side of the rectangle.

Approach & Working
As the squares are nonoverlapping, the total area of all 3 squares will be equal to the area of the rectangle.
    • Area of each square = 24/3 = 8
    • Therefore, side length of each square = √8 = 2√2
    • Thus, the longest side of the rectangle = 2√2 + 2√2 + 2√2 = 6√2

Hence, the correct answer is option D.


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Re: If a rectangle of area 24 can be partitioned into exactly 3 nonoverlap [#permalink] New post  27 May 2019, 19:09
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Bunuel 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. \(12\sqrt{2}\)


PS88502.01
Quantitative Review 2020 NEW QUESTION



Since the 3 nonoverlapping squares have equal area, the area of each square is 24/3 = 8, and thus the side of each square is √8. Therefore, the rectangle’s width is √8, and its length is 3 times the width, or 3√8 = 3(2√2) = 6√2.

Answer: D
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Re: If a rectangle of area 24 can be partitioned into exactly 3 nonoverlap [#permalink] New post  21 Jun 2019, 08:44
Bunuel 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. \(12\sqrt{2}\)

Area of rectangle: L*W = 24

Since the areas of the 3 squares are equal, we can divide by 3 to get the area of 1 square.
L*W/3 = 8
side² = 8
side = 2√(2)
This is trap answer A
B, C are also out because the side length won't be an integer, so D, E are left.
The side of the square is the shorter side of the rectangle, to find the other side multiply 2√2 * 3 = 6√2
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Re: If a rectangle of area 24 can be partitioned into exactly 3 nonoverlap [#permalink] New post  21 Jun 2019, 08:49
Bunuel 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. \(12\sqrt{2}\)


PS88502.01
Quantitative Review 2020 NEW QUESTION


Area of each square: 8, so side: 2(Root 2)
So, width of the Rectangle: 2(Root 2)
& Length: 3 * 2(Root 2)= D. \(6\sqrt{2}\)
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ThatDudeKnows
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Re: If a rectangle of area 24 can be partitioned into exactly 3 nonoverlap [#permalink] New post  10 Jun 2022, 13:48
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Bunuel 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. \(12\sqrt{2}\)


PS88502.01
Quantitative Review 2020 NEW QUESTION


The rectangle is is 3x on the longer side and x on the shorter side. Let's glance at the answer choices.
If the longer side is 8, the shorter side is 8/3, which is shorter than 3. 8*shorterthan3 is too small. C is wrong and so are A and B.
E looks bananas long. \(12\sqrt{2}*4\sqrt{2}\) is too big even if we ignore the \(\sqrt{2}\) parts. E is wrong.
Only D is left.

Answer choice D.

Use the answer choices!
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Re: If a rectangle of area 24 can be partitioned into exactly 3 nonoverlap [#permalink]
10 Jun 2022, 13:48
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