Question

What are the possible expressions for the dimensions of the cuboids whose volumes are given below?

Volume : 12ky2 + 8ky – 20k

Answer 1

Volume of cuboid = Length × Breadth × Height

The expression given for the volume of the cuboid has to be factorised. One of its factors will be its length, one will be its breadth, and one will be its height.

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)