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

(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)