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Question: Answered & Verified by Expert
A regular octagon is formed by cutting congruent isosceles right- angled triangles from the corners of a square. If the square has side- length 1 , the side - length of the octagon is -
MathematicsBasic of MathematicsKVPYKVPY 2012 (SA)
Options:
  • A $\frac{\sqrt{2}-1}{2}$
  • B $\sqrt{2}-1$
  • C $\frac{\sqrt{5}-1}{4}$
  • D $\frac{\sqrt{5}-1}{3}$
Solution:
1456 Upvotes Verified Answer
The correct answer is: $\sqrt{2}-1$


Here $2\left(\frac{1-x}{2}\right)^{2}=x^{2}$
$(1-x)^{2}=2 x^{2}$
$\mathrm{x}=\sqrt{2}-1$

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