A box has a volume of 192 cubic inches, a length that is twice as long as is width, and a height that is 2 inches greater than the width.what are the dimensions of the box
Accepted Solution
A:
Volume of box has a formula of: length × width × height
We know from the question that the length is 2 times of the width, and the height is 2inches greater than the width.
Since all 3 sides are relative to the width, let x be the width, Width = x inches Length = 2x inches Height = (x + 2) inches
We know that Volume = Length × Width × Height: 192 inches^3 = 2x × x × (x + 2) inches 192 = 2x × x × (x + 2) 192 = 2x^2 × (x + 2) 192 =2x^3 + 4x^2 {Divide both sides of equation by 2} 96 = x^3 + 2x^2 {Bring all values to one side of the equation by subtracting 96 from both sides} 0 = x^3 + 2x^2 - 96 {Factorise} (x - 4) (x^2 + 6x + 24) = 0 {Divide both sides by (x^2 + 6x + 24). 0 divided by (x^2 + 6x + 24) will give 0} (x - 4) = 0 x = 4 {x^2 + 6x + 24 has no real x-value, so leave it. Do let me know if you'd like me to prove that (x^2 + 6x + 24) has no real x-value :)