SOLUTION: An open box is formed from a square piece of cardboard, by removing squares of side 7 in. from each corner and folding up the sides. If the volume of the carton is then 56 in3, wha

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Question 523185: An open box is formed from a square piece of cardboard, by removing squares of side 7 in. from each corner and folding up the sides. If the volume of the carton is then 56 in3, what was the length of a side of the original square of cardboard
Answer by mananth(16946) About Me  (Show Source):
You can put this solution on YOUR website!
let the length of the side be x in
7 in is cut off from both ends
the sides become x-14
The box will have dimensions (x-14), (x-14) & 7 height
The Volume of box = L*W*H
Volume = (x-14)*(x-14)*7
Volume = (x-14)^2*7
56 = (x^2-28x+196)*7
/7
8=x^2-28x+196
x^2-28x+188=0
Find the roots of the equation by quadratic formula

a= 1 ,b= -28 ,c= 188

b^2-4ac= 784 + -752
b^2-4ac= 32
x=%28-b%2B-sqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-b%2Bsqrt%28b%5E2-4ac%29%29%2F%282a%29
x1=%28-12%2B21%29%2F%2812%29
x1=( 28 + 5.66 )/ 2
x1= 16.83
x2=( 28 -5.66 ) / 2
x2= 11.17
The side cannot be 11.17 since we are cutting off 14 inches
The original side is 16.83 in
....
CHECK
16.83-14=2.83
Box dimension 2.83,2.83,7
Volume =2.83*2.83*7
Volume = 56 in^3