May 22, 2000
Problem of the Month

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

Send any comments or questions to: David Pleacher