What are the possible expressions for the dimensions of the cuboids whose volume are given?
Volume: $12 k y^{2} + 8 k y - 20 k$

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Solution

here function of volume is in $y$ & $k$

so, here Function $v (k, y) = 12 k y^{2} + 8 k y - 20 k$

$v (k, y) = 4 k (3 y^{2}) + 4 k (2 y) + 4 k (- 5)$

$= 4 k (3 y^{2} + 2 y - 5)$

$= 4 k (3 y^{2} + 5 y - 3 y - 5)$

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

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

so, the dimension of the cuboids will be $4 k, y - 1$ & $3 y + 5$

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Similar questions

What are the possible expressions for the dimensions of the cuboid whose volumes are given below?
(i) Volume: ${3 x}^{2} - 12 x$

(ii) Volume: $12 k y^{2} + 8 k y - 20 k$

\begin{matrix} \begin{matrix} V o l u m e : 3 x^{2} - 12 x \end{matrix} (i) \end{matrix} \begin{matrix} \begin{matrix} V o l u m e : 12 k y^{2} + 8 k y - 20 k \end{matrix} (i i) \end{matrix}

V o l u m e : 12 k y^{2} + 8 k y - 20 k

What are the possible expressions for the dimensions of cuboid , whose volume is : 12ky^2 +8ky- 20 k?

3 x^{2} - 12 x

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