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What are the possible expressions for the dimensions of the cuboids whose volumes are given below?
(i) $\boxed{Volume:\ 3\ x^{2} -12x}$
(ii) $\boxed{Volume\ :\ 12k\ y^{2} +8k\ y-20k}$
To do :
We have to find the possible expressions for the dimensions of the cuboids whose volumes are given.
Solution :
We know that,
Volume of a cuboid of length $l$, breadth $b$ and height $h$ is $lbh$.
Therefore, factorizing the given expressions, we get,
(i) Volume $=3x^2 - 12x$
$=3x(x-4)$
$=3 \times x \times (x-4)$
Hence, possible expressions for the dimensions of the cuboid whose volume is $3x^2 - 12x$ are $3, x$ and $(x-4)$.
(ii)  Volume$=12ky^2+8ky-20k$
$=4k(3y^2+2y-5)$
$=4k(3y^2+5y -3y-5)$
$=4k(y (3y+5)-1(3y+5))$
$=4k( 3y +5) (y-1)$
Hence, possible expressions for the dimensions of the cuboid whose volume is $4k$ are $(3y+5)$ and $(y-1)$.
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