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 value of x = 3.

Length = 4 feet and Width = 5 feet

Explanation:

Height of the box = 2 ft

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

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

Volume of the box = 40 cubic feet

Now, VOLUME OF CUBE = LENGTH x WIDTH x HEIGHT

`\implies 40 = 2 * (3x-5) * (2x-1)\\\implies 20 = 3x(2x-1)) -5 (2x-1) = 6x^2 - 3x -10x +5 = 6x^2 - 13x + 5\\\implies 6x^2 - 13x -15 = 0`

Now, solving for the value of x, we get:

`6x^2 -13 x - 15 = 6x^2 -18x + 5x - 15 = 0\\\implies6x(x-3) + 5(x-3) = 0\\\implies (x-3)(6x+5) = 0`

⇒ Either x-3 = 0, or ( 6x+5) = 0

⇒ Either x = 3, or x = -5/6

As x = SIDE OF A CUBE ,so it CANNOT be negative.

⇒x = 3

So, length = (3x-5) = 3(3) -5 = 9-5 = 4 units

Width = (2x-1) = 2(3) -1 = 5 units