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705-805 (Hard)|   Geometry|      
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Bunuel
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What is the ratio of longest diagonal to the shortest diagonal in a re 01 May 2020, 03:49
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75% (hard)

Question Stats:

55% (02:27) correct 45% (02:27) wrong based on 87 sessions

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What is the ratio of longest diagonal to the shortest diagonal in a regular octagon (an eight-sided polygon)?

A. 3 : 1
B. 2 : 1
C. √3 : 1
D. √2 : 1
E. 2 : √3

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D
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What is the ratio of longest diagonal to the shortest diagonal in a re 01 May 2020, 04:48
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Bunuel
What is the ratio of longest diagonal to the shortest diagonal in a regular octagon (an eight-sided polygon)?

A. 3 : 1
B. 2 : 1
C. √3 : 1
D. √2 : 1
E. 2 : √3

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regular octagon:
exterior angle = 360 /8 = 45
interior angle = 180 - 45 = 135
Attachment:
img.png
img.png [ 22.26 KiB | Viewed 12531 times ]
in the figure the two shortest diagonals will be same length x and longer diagonal be y.
as the triangle is right angled.
y = \(\sqrt{2}\)x
y/x = \(\sqrt{2}:1\)
Ans: D
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What is the ratio of longest diagonal to the shortest diagonal in a re 02 May 2020, 05:40
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Bunuel
What is the ratio of longest diagonal to the shortest diagonal in a regular octagon (an eight-sided polygon)?

A. 3 : 1
B. 2 : 1
C. √3 : 1
D. √2 : 1
E. 2 : √3

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Please enjoy the step-by-step approach in the video solution.

Answer: Option D

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What is the ratio of longest diagonal to the shortest diagonal in a re 03 May 2020, 16:15
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Please See The Attached File.

If you draw this octagon inside the circle, the longest diagonal will 2R.
As you see the right-angled triangle in the picture, two other sides of the triangle is the shortest diagonal of the octagon.
---> \(x^{2} + x^{2} = (2R)^{2}\)

\(2x^{2} = 4R^{2}\)

\(x = √2R\)

\(\frac{Diagonal_{Longest}}{ Diagonal_{Shortest} }= \frac{2R}{√2R}= \frac{√2}{1}\)

Answer (D).
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What is the ratio of longest diagonal to the shortest diagonal in a re 04 Jun 2021, 10:18
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I find the easiest way to consider the octagon circumscribed in a circle. As it is a regular polygon, naturally, the longest distance inside the octagon is the longest length of the circle = diameter. From here it can be seen that longest diagonal and shortest diagonal form one leg and hypotenuse of an isosceles right triangle.

Ratio Sqrt 2 : 1
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What is the ratio of longest diagonal to the shortest diagonal in a re 18 Sep 2024, 06:40
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