Question

MATHEMATICS
What are the possible expressions for the dimensions of the cuboids whose volumes
are given below?
Volume : 3x2 - 12x
Volume : 12ky2 + Sky - 20k
​

Answer 1

Answer:

Step-by-step explanation: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...