SOLUTION: Tracey is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Tracey is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base      Log On


   

Question 163347: Tracey is going to make an open-top box by cutting equal squares from the four corners of an 11 inch by 14 inch sheet of cardboard and folding up the sides. If the area of the base is to be 80 square inches, then what size square should be cut from each corner?
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
11*14=154
(11-2X)(14-2X)=80
154-50X+4X^2=80
4X^2-50X+154-80
4X^2-50X+74=0
2(2X^2-25X+37)=0
x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+
X=(25+-SQRT[-25^2-4*2*37])/2*2
X=(25+-SQRT[625-296])/4
X=(25+-SQRT329)/4
X=(25+-18.13836)/4
X=25-18.13836)/4
X=6.8616/4
X=1.71541 INCH SQUARES NEED TO BE CUT FROM EACH CORNER.
PROOF:
(11-2*1.71541)(14-2*1.71541)=80
(11-3.43)(14-3.43)=80
7.57*10.57=80
80=80