Question 17103: A rectangular game board is made up of two species of wood. The pine center section is 4 inches wides and 12 inches long. A redwood border of equal width on all sides surrounds the pine center section, and the area of the redwood section is 16 square inches. How wide is the redwood border?
Answer by rapaljer(4671)   (Show Source):
You can put this solution on YOUR website! Let x = width of the redwood border on each side, top, and bottom of the board.
Total dimensions of the board:
width = 4 inches + x on top and bottom = 4+2x
length = 12 inches + x on each side = 12 + 2x
Total area = W*L = (4+2x)*(12+2x)= Pine + Redwood = 4*12 + 16
Multiply out: 48 + 8x + 24x + 4x^2 = 48 + 16
4x^2 + 32x - 16 = 0
Factor out the 4:
4(x^2 + 8x -4)= 0
Now, I really thought the person who made up this problem would have made it come out even--they usually do, you know!! But I've checked this work a few times, and I can't find an error. I'll assume that the answer does NOT come out even--real life, you know, doesn't always come even!
Solve x^2 + 8x -4=0 by completing the square, where half of 8 is 4, and 4^2 = 16 (or you can also solve using the quadratic formula!):
x^2 + 8x + _____ = 4 + _____
x^2 + 8x + 16 = 4+16
(x+4)^2 = 20
Take the square root of each side:
Reject negative answer, so  = .472 approximately
I hope this is correct. If anyone finds an error please let me know.
R^2 at SCC
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