Question

Find the possible expression for the dimensions of the cuboids whose volume is 12ky^2+8ky-20k​

Answer 1

Answer:

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.

(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)

Answer 2

$\large\sf{4k(3 {y}^{2} + 2y - 5)}$

$\large\sf{4k( {y}^{2} + 5y - 3y - 5)}$

$\large\sf{4k(y(3y + 5)-1(3y - + 5))}$

$\large\sf{4k(y-1)(3y+5)}$

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$\huge\therefore$ ,

$\huge\sf\green{l=4k}$

$\huge\sf\pink{b=(y-1)}$

$\huge\sf\purple{h=(3y+5)}$