Question

. The volume of a box is 405 cubic units. The length is x units, the width 4 units greater than the length, and the height is 9 units. Find the length and width of the box.

Answer 1

length = 5

width = 9

Explanation:

V = lwh

let 'x' = length

let '4+x' = width

9 = height

405 = 9x(4+x)

405 = 36x + 9x²

this is a quadratic equation: 9x² + 36x - 405 = 0

factor out a 9 to get:

9(x² + 4x - 45) = 0

9(x-5)(x+9) = 0

one root is 5 and the other is -9

since distance cannot be negative we use 5 as the length and 9 is the width