### The corners of a square with side 10 is cut away to form an octagon with all sides equal. What is the length of a side of the octagon so formed?

**Answer:**

10 |

1 + √2 |

**Step by Step Explanation:**

- Let ABCD be a square and PQRSTUVW is a octagon with equal sides constructed within a square.
- As we have to construct an octagon with equal sides we will take AP = AQ = QB = BR = BS = UC = CT = DV = DW.
- Let AP = AQ = x [Side of the square cut]

and PQ = y [Side of the regular octagon] - As all sides of the octagon are equal.

QR = RS = ST = TU = UV = VW = WP = PQ = y - As the length of the square is 10 cm,

2x + y = 10 ................(1) - Applying Pythagoras to the right angled triangle APQ,

y^{2}= x^{2}+ x^{2}= 2x^{2}

or y = x √2...............(2) - Solving (1) and (2), we get y =

.10 1 + √2 - Thus, the length of the side of the octagon so formed is
10 1 + √2