The possible expressions for the dimensions of the cuboids whose volume is $3 x ² – 12 x$ . Then, the expression of length is 3, breadth and height .

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Detailed Solution

The possible expressions for the dimensions of the cuboids whose volume is

3 x ² – 12 x

. Then, the expression of length is 3, breadth x and height (x-4).
Given volume of cuboid is

3 x ² – 12 x

.
Since, the volume is the product of length, breadth, and height therefore by factorizing the given volume, we can know the length, breadth and height of the cuboid.
First, we determine all the factors of the given polynomial by splitting the middle term and then consider any of the factors as any of the dimensions.
Take 3x as common:

3 x ² – 12 x

3 x (x - 4)

Write the above expression as length, breadth and height:
Length =3
Breadth = x
Height =(x – 4)
Hence, possible expression for length = 3.
Possible expression for breadth = x.
Possible expression for height = (x – 4).
The possible expressions for the length, breadth, and height of the following cuboid is 3, x, and (x - 4).

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