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
:
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( 300, 200, -5, 5, -10, 10, 2x^3+7x^2+3x-50) }}} 


 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