You are given a square, each of whose sides measure
x inches.
If the corners of the square are cut off so that a
regular octagon remains, how long is each side of
the resulting octagon in terms of x?
Solution to the Problem:
Answer is (\/2 - 1)x or .414x.
The four corner triangles are isosceles right
triangles.
Let each of the eight sides of the octagon be y.
Then AB = y.
So, AC = y divided by the square root of 2.
So each side of the square would equal:
x = y + (y\/2) / 2 + (y\/2) / 2
x = y + y\/2
solving for y:
y = x / (1 + \/2)
Rationalizing the denominator gives you
y = (\/2 - 1) x or .414x
Correctly solved by:
| 1. Kirstine Wynn | Winchester, VA |
| 2. Tom Marino | Winchester, VA |
| 3. Chip Crawford | Winchester, VA |
| 4. Josh Grewal | Winchester, VA |