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19 Aug 2021, 08:00
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E
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Difficulty:
85%
(hard)
Question Stats:
47% (02:04) correct
53%
(01:52)
wrong
based on 214
sessions
History
Date
Time
Result
Not Attempted Yet
Rectangle given above is divided into eight squares. If the area of the yellow square in the center is 1, what is the area of the rectangle ?
A. 14.5
B. 29
C. 40
D. 41
E. 58
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M37-35
Attachment:
Untitled9.png
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23 Nov 2021, 06:45
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Official Solution:
Rectangle given above is divided into eight squares. If the area of the yellow square in the center is 1, what is the area of the rectangle ?
A. \(14.5\)
B. \(29\)
C. \(40\)
D. \(41\)
E. \(58\)
Say the side length of a red square in \(x\). Then:
The side length of a green square will be \(x+x=2x\);
The side length of a pink square will be \(x+x+1=2x+1\);
The side length of a purple square will be \((2x+1)+1=2x+2\);
The side length of a blue square will be \(2x+x-1=3x-1\).
Next, the length of the rectangle if we measure top side will be \((2x+1)+(2x+2)=4x+3\) and if we measure bottom side it will be \(2x+(3x-1)+(3x-1)=8x-2\). Equate:
Equate: \(4x+3=8x-2\). Solve: \(x=\frac{5}{4}\).
The area of the rectangle = \((4x+3)(5x+1)=58\).
Answer: E
Rectangle given above is divided into eight squares. If the area of the yellow square in the center is 1, what is the area of the rectangle ?
A. \(14.5\)
B. \(29\)
C. \(40\)
D. \(41\)
E. \(58\)
Say the side length of a red square in \(x\). Then:
The side length of a green square will be \(x+x=2x\);
The side length of a pink square will be \(x+x+1=2x+1\);
The side length of a purple square will be \((2x+1)+1=2x+2\);
The side length of a blue square will be \(2x+x-1=3x-1\).
Next, the length of the rectangle if we measure top side will be \((2x+1)+(2x+2)=4x+3\) and if we measure bottom side it will be \(2x+(3x-1)+(3x-1)=8x-2\). Equate:
Equate: \(4x+3=8x-2\). Solve: \(x=\frac{5}{4}\).
The area of the rectangle = \((4x+3)(5x+1)=58\).
Answer: E
General Discussion
19 Aug 2021, 08:47
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Rectangle given above is divided into eight squares. If the area of the yellow square in the center is 1, what is the area of the rectangle ?
Attachment:
Screenshot 2021-08-19 at 9.12.49 PM.png [ 26.11 KiB | Viewed 5883 times ]
Length of the rectangle = 2(4-y) + 1 + 2y - 1 = 8 - 2y + 1 + 2y - 1 = 8 = (2y-1) + (2y-2) = 4y - 3
y = 11/4 = 2.75
Width of the rectangle = y + (2y-1) = 3y- 1 = 33/4 -1 = 7.25
Area of the rectangle = 8*7.25 = 58
IMO E
