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# What are the possible expressions for the dimensions of the cuboid whose volumes is given below? (ii) Volume: 12ky ^2 + 8ky - 20k

16.(ii)  What are the possible expressions for the dimensions of the cuboid whose volumes is given below?

(ii)

 Volume :    $12ky^2 + 8ky - 20k$
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We know that

Volume of cuboid is =  $length \times breadth \times height$

It is given that volume  =  $12ky^2+8ky-20k$

Now,

$\Rightarrow 12ky^2+8ky-20k = k(12y^2+8y-20)$

$= k(12y^2+20y-12y-20)$

$= k\left(4y(3y+5)-4(3y+5) \right )$

$= k(3y+5)(4y-4)$

$= 4k(3y+5)(y-1)$

Therefore,one of the possible answer is possible

Length = $4k$  and  Breadth = $(3y+5)$  and  Height =  $(y-1)$

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