SOLUTION: A regular octagon with side length "a" cm can be made by cutting off the four corners of a square board. How long should the sides of the board be? Note: 45-45-90 Special triang

Algebra ->  Pythagorean-theorem -> SOLUTION: A regular octagon with side length "a" cm can be made by cutting off the four corners of a square board. How long should the sides of the board be? Note: 45-45-90 Special triang      Log On


   

Question 773264: A regular octagon with side length "a" cm can be made by cutting off the four corners of a square board. How long should the sides of the board be?
Note: 45-45-90 Special triangle
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
This set of steps really needs a drawing to make clear what it means, but
The side of the square is made of a%2Bx+%2Bx, where x is the unknown length leg of one of the 45-45-90 triangles. Hypotenuse of the 45-45-90 triangle is also length a. Pythagorean Theorem gives us x%5E2%2Bx%5E2=a%5E2,
2x%5E2=a%5E2
x%5E2=%281%2F2%29a%5E2
x=a%2Asqrt%281%2F2%29
x=%28a%2F2%29sqrt%282%29
Side of square is then a%2B2x=a%2Ba%2Asqrt%282%29


----this picture is not finished-----
____near top of octagon________
not drawn to scale