SOLUTION: The length of a rectangular box is 1 inch more than twice the height of the box, and the width is 3 inches more than the height. If the volume of the box is 50 cubic inches, find t

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Question 621576: The length of a rectangular box is 1 inch more than twice the height of the box, and the width is 3 inches more than the height. If the volume of the box is 50 cubic inches, find the dimensions of the box.
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
The length of a rectangular box is 1 inch more than twice the height of the box, and the width is 3 inches more than the height.
If the volume of the box is 50 cubic inches, find the dimensions
:
Let x = the height of the box
:
"The length of a rectangular box is 1 inch more than twice the height"
L = 2x+1
:
"width is 3 inches more than the height."
W = x+3
:
L * W * H = 50
(2x+1)*(x+3)*x = 50
FOIL
(2x^2 + 6x + x + 3)*x = 50
x(2x^2 + 7x + 3) = 50
2x^3 + 7x^2 + 3x - 50 = 0
Plot this on your graphing calc,
+graph%28+300%2C+200%2C+-5%2C+5%2C+-10%2C+10%2C+2x%5E3%2B7x%5E2%2B3x-50%29+

see that the solution is x=2 is the height
then
2 cm = the height
2(2)+1 = 5 cm is the length
2 + 3 = 5 cm is the width