Question

A packing company is doing an inventory of boxes. Their most popular box is display below: 2ft,(3x-5)ft,(2x-1)ft you can use the formula V= lwh to find the volume of the box. The volume of the box is 40ft3.What is the value of x ? Find the length and width of the box.

Answer 1

The length will be 5 feet, width will be 4 feet.

Explanation:

Given:

volume of the box = 40 ft^3

Length of the box = (2x-1)ft

Width of the box = (3x-5)ft

Height of the box = 2ft,

To Find:

The length and width of the box = ?

Solution:

We know that,

`\text{volume of the box} = Length * breadth * height`

`40= (2x-1) * (3x-5) * 2`

`40 = (2x-1) *(6x-10)`

`40 = 12x^2 - 20x - 6x +10`

`40 = 12x^2 - 26x +10`

`12x^2 - 26x +10-40 = 0`

`12x^2 -26x -30 = 0`-----------------------(1)

Solving eq(1) by quadratic equation formula

`x = (-b \pm √(b^2-4ac))/(2a)`

Substituting the values

`x = (-(-26) \pm √((-26)^2-4(12)(-30)))/(2(12))`

`x = (26 \pm √(676 -4(-360)))/(24)`

`x = (26 \pm √(2116))/(24)`

`x = (26 \pm 46)/(24)`

`x = (26 + 46)/(24)`
`x = (26-46)/(24)`

`x =(72)/(24)`
`x = (-20)/(24)`

x = 3 x =-0.833

Neglecting the negative value,

we have x = 3

Then the length will be

(2(3)-1) = (6-1) =5 ft

The Width will be

(3(3)-5) = (9-5) = 4 ft