Answer:
The value of x = 3.
Length = 4 feet and Width = 5 feet
Step-by-step 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 \times (3x-5) \times (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](https://tex.z-dn.net/?f=%5Cimplies%2040%20%3D%202%20%5Ctimes%20%283x-5%29%20%5Ctimes%20%282x-1%29%5C%5C%5Cimplies%2020%20%3D%203x%282x-1%29%29%20-5%20%282x-1%29%20%3D%206x%5E2%20-%203x%20-10x%20%2B5%20%20%3D%206x%5E2%20-%2013x%20%2B%205%5C%5C%5Cimplies%20%206x%5E2%20-%2013x%20-15%20%3D%200)
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](https://tex.z-dn.net/?f=6x%5E2%20-13%20x%20-%2015%20%20%3D%206x%5E2%20-18x%20%2B%205x%20-%2015%20%3D%200%5C%5C%5Cimplies6x%28x-3%29%20%2B%205%28x-3%29%20%3D%200%5C%5C%5Cimplies%20%28x-3%29%286x%2B5%29%20%3D%200)
⇒ 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