Question

What are the possible expressions for the dimensions of the cuboid whose
volume is 3x2-12x

please tell the answer
Only if correct​

Answer 1

Problem

based on geometrical figure:

First

we determine all the factors of the given polynomial by splitting middle term and then consider any of

the factor as any of the dimension.

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Solution:

 

(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)

 

Hence,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)

[By

middle term splitting]

=

4k(3y² +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)

 

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Hope this will help you...

Answer 2

${\fbox{\huge\sf{\pink{An}\purple{sW}\green{eR}}}}$

Volume 3x² – 12x

= 3x(x – 4)

∴ Factors are 3, x, and x – 4

Now, if length = 3, breadth = x and height = x – 4

if length =3, breadth = x – 4, height = x

if length = x, breadth = 3, height = x – 4

if length = x, breadth = x – 4, height = 3

if length = x – 4, breadth = 3, height = x

if length – x – 4, breadth = x, height = 3