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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Updated on: 10-Oct-2022

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