the height of a box is 6 inches. the length is three inches more than the width. find the width if the volume is 240 cubic inches
Volume = HLW
Volume = 240
H = 6
If W = x, then L = x +3
240 = 6x(x+3)
40 = x^2 + 3x
0 = X^2 + 3x - 40
Solve for x.
To find the width of the box, we need to use the information given and set up an equation.
Let's assume the width of the box is w inches.
According to the information given, the length is three inches more than the width. So, the length of the box would be w + 3 inches.
The height of the box is given as 6 inches.
To find the volume of the box, we multiply its length, width, and height:
Volume = Length * Width * Height
Given that the volume is 240 cubic inches:
240 = (w + 3) * w * 6
Now, we can solve this equation to find the width of the box.
First, distribute the 6 to the terms inside the parenthesis:
240 = 6w^2 + 18w
Rearrange the equation to form a quadratic equation equal to zero:
6w^2 + 18w - 240 = 0
Divide through by 6 to simplify the equation:
w^2 + 3w - 40 = 0
Now, we can solve this quadratic equation by factoring, completing the square, or using the quadratic formula.
Factoring this equation, we have:
(w + 8)(w - 5) = 0
Setting each factor equal to zero:
w + 8 = 0 or w - 5 = 0
Solving for w:
w = -8 or w = 5
Since the width cannot be negative, the width of the box is 5 inches.