Answer to May 22, 2000 Problem

The Corners of a Square

 
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