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)