What are the possible expressions for the dimensions of the cuboids whose volumes are given below? (i) Volume : 3x² - 12x
(ii) Volume : 12ky² + 8ky - 20k

Answer

(i) Volume : 3x² - 12x 
Since, volume is product of length, breadth and height therefore by factorizing the given volume, we can know the length, breadth and height of the cuboid. 
3x² - 12x
= 3x(x - 4)
Possible expression for length = 3
Possible expression for breadth = x
Possible expression for height = (x - 4)

(ii) Volume : 12ky² + 8ky - 20k 
Since, volume is product of length, breadth and height therefore by factorizing the given volume, we can know the length, breadth and height of the cuboid. 
12ky² + 8ky - 20k
= 4k(3y² + 2y - 5)
= 4k(3y² +5y - 3y - 5)
= 4k[y(3y +5) - 1(3y + 5)]
= 4k (3y +5) (y - 1)
Possible expression for length = 4k
Possible expression for breadth = (3y +5)
Possible expression for height = (y - 1)