**Q.16. **What are the possible expressions for the dimensions of the cuboids whose volumes are given below?

(i) Volume: 3x^{2} - 12x (ii) Volume: 12ky^{2} + 8ky - 20k

**Solution:**

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.

(i) Volume: 3x^{2} - 12x

We can write, 3x^{2} - 12x = 3x(x - 4)

Hence, possible expression for length = 3

Possible expression for breadth = x

Possible expression for height = (x - 4)

(ii) Volume: 12ky^{2} + 8ky - 20k

We can write, 12ky^{2} + 8ky - 20k = 4k(3y^{2} + 2y - 5)

= 4k(3y^{2} +5y - 3y - 5)

= 4k[y(3y +5) - 1(3y + 5)]

= 4k (3y +5) (y - 1)

Hence, possible expression for length = 4k

Possible expression for breadth = 3y +5

Possible expression for height = y - 1