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505-555 Level|   Geometry|               
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Bunuel
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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Bunuel
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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Bunuel
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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Bunuel
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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