Question 17103
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:
{{{x+4 = 0+-sqrt(20)}}}
{{{x=-4+- 2sqrt(5)}}}


Reject negative answer, so {{{x= -4 + 2sqrt(5)}}} = .472 approximately


I hope this is correct.  If anyone finds an error please let me know. 


R^2 at SCC