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

Answer:

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

Step-by-step 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,

$\text{volume of the box} = Length \times breadth \times height$

$40= (2x-1) \times (3x-5) \times 2$

$40 = (2x-1) \times(6x-10)$

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

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

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

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

Solving eq(1) by quadratic equation formula

$x = \frac{-b \pm \sqrt{b^2-4ac}}{2a}$

Substituting the values

$x = \frac{-(-26) \pm \sqrt{(-26)^2-4(12)(-30)}}{2(12)}$

$x = \frac{26 \pm \sqrt{676 -4(-360)}}{24}$

$x = \frac{26 \pm \sqrt{2116}}{24}$

$x = \frac{26 \pm 46}{24}$

$x = \frac{26 + 46}{24}$                                       $x = \frac{26-46}{24}$

$x =\frac{72}{24}$                                            $x = \frac{-20}{24}$

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