The height of a rectangular prism is 3ft. the length and width can be expressed as x-1 and x+4. if the volume of the prism is 198ft^3, find the value of x

Formula

Volume = Length x Width x Height


Apply Formula

198 = 3(x-1)(x+4)


Divide by 3 through

66 = (x-1)(x+4)


Remove brackets

66 = x² + 4x - x - 4
66 = x² + 3x - 4


Take away 66 from both sides

0 = x² + 3x - 4 - 66
x² + 3x - 70 = 0


Factorise the quadratic

(x - 7)(x + 10) = 0
x = 7 or x = -10 (rejected, length cannot be negative)


Answer : x = 7