a rectangular solid has a volume of 640 cubic units. the width is 3 units more than the height and the length is 1 unit more than three times the height. find the dimensions of the solid.

Answer 1

height --- x
width ---- x+3
length ---- 3x + 1

V = lwh
x(x+3)(3x+1) = 640
x(3x^2 + 10x + 3) = 640
3x^3 + 10x^2 + 3x - 640 = 0
wow, ....

tried x = ±1 , no
tried x = ±2 , no
tried x = ±4 , no
tried x = ± 5, YEAHHH x = 5 worked

(x-5)(x^2 + 25x + 128) = 0
the quadratic has no real solutions for x

x=5

height --- 5
widht ---- 8
length --- 16

check: 5x8x16 = 640