2019 · Q76
The corners of a square of side ‘a’ are cut away so as to form a regular octagon. What is the side of the octagon?
Elementary MathematicsQuadrilaterals and Polygons
- Aa(√2 - 1)
- Ba(√3 - 1)
- Ca/(√2 + 2)
- Da/3
Explanation
Cut a length x from each corner: the cut triangle has hypotenuse x√2, which must equal the remaining middle segment a−2x. So a = x(2+√2), x = a/(2+√2), and the octagon side is x√2 = a√2/(2+√2) = a(√2−1). (Note a/(√2+2) rationalises to a(2−√2)/2, a different value — the common trap.)