SOLUTION: Hi, I need help solving this problem. A rectangular piece of cardboard 11 inches by 14 inches is made into a box by cutting idential squares from each corner and folding up the

Algebra ->  Quadratic Equations and Parabolas -> SOLUTION: Hi, I need help solving this problem. A rectangular piece of cardboard 11 inches by 14 inches is made into a box by cutting idential squares from each corner and folding up the      Log On


   

Question 205148: Hi, I need help solving this problem.
A rectangular piece of cardboard 11 inches by 14 inches is made into a box by cutting idential squares from each corner and folding up the sides. If the bottom of the box turns out to haave an area of 80 in^2, what size squares were cut from the corners?

I am setting up my problem as: 80 = (w-11)(w-14) but I am not sure if I am barking up the wrong alley (so to speak). Any help or suggestions would be greatly appreciated.
Thank you - Lori
Answer by checkley77(12844) About Me  (Show Source):
You can put this solution on YOUR website!
(11-2x)(14-2x)=80
154-28x-22x+4x^2=80
4x^2-50x+154-80=0
4x^2-50x+74=0
Using the quadratic equation x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+ we get:
x=(50+-sqrt[-50^2-4*4*74])/2*4
x=(50+-sqrt[2,500-1,184])/8
x=(50+-sqrt1,316)/8
x=(50+-36.2767)/8
x=(86.2767)/8
x=10.78 not an ans.
x=(50-36.2767)/8
x=13.7233/8
x=1.7154 in. is the size of the square removed from the 4 corners.
Proof:
(11-2*1.7154)(14-2*1.7154)=80
(11-3.43)(14-3.43)=80
7.57*10.57=80
80~80