company will enclose a rectangular area of 12 comma 600 ft squared12,600 ft2 in the rear of its plant. One side will be bounded by the building and the other three sides by fencing, as shown to the right. If 320 ft320 ft of fencing will be used, what will be the dimensions of the rectangular area?
2 x + y = 320
x y = 12,600 so y = 12,600/x
2 x + 12,600/x = 320
x^2 + 6,300 = 160 x
x^2 - 160 x + 6,300 = 0
x = [160+/-sqrt(25600-25200)]/2
x = [ 160 +/- 20] /2
x = 90 or 70
try 90
then y = 140
2x + y = 320 Yes, that works
try 70
y = 180
2x+ y = 140 + 180 = 320, Yes that works