Question

A square, whose side is 2 m, has its corners cut away so as to form an octagon with all sides equal. Then the length of each side of the octagon, in metres, is:

• A. $\frac{\sqrt{2}}{\sqrt{2} + 1}$
• B. $\frac{2}{\sqrt{2} + 1}$
• C. $\frac{2}{\sqrt{2} - 1}$
• D. $\frac{\sqrt{2}}{\sqrt{2} - 1}$

Hint:

In regular octagon formation from square, use symmetry and corner right-triangle properties to relate side lengths.

Answer 1

The Correct Option is B

Let each cut-off be length $x$. Each octagon side consists of original square side minus two $x$ plus diagonal of cut square ($x\sqrt{2}$). Equation: $2 - 2x + x\sqrt{2} = s$ (side length of octagon). Geometry shows $x = 2 - 2s$. Substituting and solving gives $s = \frac{2}{\sqrt{2} + 1}$.