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20 Sep 2018, 22:38
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Difficulty:
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Question Stats:
52% (02:25) correct
48%
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based on 71
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ABCD is a square of side 4 inch. If each corner of square is cut identically so that resultant structure becomes regular eight sided polygon. What is length of side of octagon?
A) \(4/ (2-√2)\)
B) \(2√2/ (√2+1)\)
C) \(4(√2-1)\)
D) \(4(√2+1)\)
E) \(4/ (√2-1)\)
A) \(4/ (2-√2)\)
B) \(2√2/ (√2+1)\)
C) \(4(√2-1)\)
D) \(4(√2+1)\)
E) \(4/ (√2-1)\)
Archit3110
21 Sep 2018, 01:35
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ABCD is a square of side 4 inch. If each corner of square is cut identically so that resultant structure becomes regular eight sided polygon. What is length of side of octagon?
A) 4/(2−√2)4/(2−√2)
B) 2√2/(√2+1)2√2/(√2+1)
C) 4(√2−1)4(√2−1)
D) 4(√2+1)4(√2+1)
E) 4/(√2−1)
GMATinsight I am not able to solve the question completely, below are my two cents :
Given each side of square is 4, so and it is cut equally to an octagon so lets assume it to be cut equally on each by x so now each side of the square will be ( 4-2x) , perimeter of the square shape with 8 points will be (4-2x) * 4: (16-8x) and we can deduce that each side of the octagon would be (16-8x)*1/8 : (2-x).
Each side of the octagon would be (2-x).
I am not able to solve further than this..not even sure whether my aforementioned approach is correct or not....
A) 4/(2−√2)4/(2−√2)
B) 2√2/(√2+1)2√2/(√2+1)
C) 4(√2−1)4(√2−1)
D) 4(√2+1)4(√2+1)
E) 4/(√2−1)
GMATinsight I am not able to solve the question completely, below are my two cents :
Given each side of square is 4, so and it is cut equally to an octagon so lets assume it to be cut equally on each by x so now each side of the square will be ( 4-2x) , perimeter of the square shape with 8 points will be (4-2x) * 4: (16-8x) and we can deduce that each side of the octagon would be (16-8x)*1/8 : (2-x).
Each side of the octagon would be (2-x).
I am not able to solve further than this..not even sure whether my aforementioned approach is correct or not....
21 Sep 2018, 02:01
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archish3113
Refer the figure attached for how the octagon will be obtained by chopping of fthe corners identically
Here Side of square, S = 4
and Side of Octagon, a = ?
Now, we see that each corner cut off is a right triangle with sides \(a√2\) as hypotenuse of the triangle being a
i.e. \(\frac{a}{√2}+a+\frac{a}{√2} = 4\)
i.e. \(a+\frac{2a}{√2} = a+a√2 = 4\)
i.e. \(a = 4/(√2+1) = 4(√2-1)\)
Answer: Option C
Hope this helps!!!
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