Question

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

Answer 1

Explanation:

Volume = 198 ft

length * width * height = 198

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

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

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

x*x + x*4 -1*x - 1*4 = 66 {Use FOIL method to multiply}

x² + 4x - x - 4 = 66

x² + 3x - 4 =66

x² + 3x - 4 - 66 = 0

x² + 3x - 70 = 0

Now factorize.

x² + 10x - 7x - 7*10 = 0

x(x +10) - 7(x + 10 ) = 0

(x + 10)(x - 7) = 0

x - 7 = 0 {x + 10 is ignored because measurement cannot be in negative}

x = 7

length = x - 1 = 7 - 1 = 6ft

Width = x + 4 = 7 + 4 = 11 ft