What is the ratio of longest diagonal to the shortest diagonal in a re

Question

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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ArunSharma12 · Answer

regular octagon: exterior angle = 360 /8 = 45 interior angle = 180 - 45 = 135 img.png 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

GMATinsight · Answer

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

Answer: Option D

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lacktutor · Answer

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).

Asitima · Answer

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

Ratio Sqrt 2 : 1

bumpbot · Answer

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What is the ratio of longest diagonal to the shortest diagonal in a re

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What is the ratio of longest diagonal to the shortest diagonal in a re

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