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?
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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,
y2 = x2 + x2 = 2x2
or y = x √2...............(2)
- Solving (1) and (2), we get y = .
- Thus, the length of the side of the octagon so formed is .