SOLUTION: A 12 inch metal square is to be transformed into a stop sign by snipping off the four corners. If this is done accurately, how long will the sides of the stop sign be?

Question 1029925: A 12 inch metal square is to be transformed into a stop sign by snipping off the four corners. If this is done accurately, how long will the sides of the stop sign be?
Answer by Boreal(15235) (Show Source): You can put this solution on YOUR website!
You have to draw this.
Let the size of the side of the stop sign be 12 (given).
Each part cut off is size x.
The hypotenuse of the triangle, which is the side of the stop sign, is x sqrt (2). This is because the external angles of an octagon are 45 degrees. The side of the square has been partitioned into the middle, which is x, and two parts cut off, which are each x sqrt(2)/2.
Therefore, x +x(sqrt(2)=12
x(1+sqrt(2)=12
x=12/(1+sqrt(2)
12(1-sqrt(2)/1-2, multiplying by the conjugate top and bottom, equals (12-12 sqrt(2)/-1
That is equal to 12 sqrt(2)-12=12(sqrt(2)-1) or 4.97 inches numerically.
That is the length of each side.
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