SOLUTION: I have a 48" square piece of plywood. I want to cut it into an octogon with all 8 sides equal length. How do I calculate this?

Algebra ->  Length-and-distance -> SOLUTION: I have a 48" square piece of plywood. I want to cut it into an octogon with all 8 sides equal length. How do I calculate this?      Log On


   

Question 132547: I have a 48" square piece of plywood. I want to cut it into an octogon with all 8 sides equal length. How do I calculate this?
Answer by scott8148(6628) About Me  (Show Source):
You can put this solution on YOUR website!
you have to cut the corners of the square off

the cut pieces will be 45° isosceles right triangles

the hypotenuse of a cut piece is the length of the side of the octagon

let x="side length of octagon" __ x+2(x/(sqrt(2)))=48 __ x+x(sqrt(2))=48

factoring __ x(1+sqrt(2))=48 __ dividing by (1+sqrt(2)) __ x=48/(1+sqrt(2))

x is approximately 19.88 inches

19.875 is 19 7/8, so the ends of the cuts are 14 1/16 in from the corners of the square