Question

the volume of a cuboid is given by the polynomial 3x^3-12x.find its dimensions

Answer 1

$\mathbb{ \underline{ \red{SOLUTION\: \: \: }}}$➡

$\bold{ \underline{Given \: \: : }} \\ \\ \bold{Volumn \: \: of \: \: the \: \: cuboid = 3x {}^{3} - 12x } \\ \\ \bold{ \underline{To \: \: find \: \: : }} \\ \\ \bold{Dimension \: \: of \: \: the \: \:cuboid = ?}$

_________________________________

$\bold{We \: \: know \: \: that,} \\ \\ \boxed{\bold{Volumn \: \: of \: \: a \: \: cuboid = l\times b \times h}} \\ \\ \bold{Where ,\: \: l = Length\: ;\: b =Breadth\: } \\ \bold{ \: and \: \: h = Height\: \: \: }$

$\bold{Now,} \\ \\ \bold{Volumn = 3x {}^{3} - 12x } \\ \\ \bold{ = 3x(x {}^{2} - 4) } \\ \\ \bold{ = 3x(x {}^{2} - 2 {}^{2}) } \\ \\ \bold{ = 3x(x + 2)(x - 2)}$

$\bold{So, \: \: the \: \: dimention \: \: of \: \: the \: \: cuboid \: \: are} \\ \\ \bold{3x \:, \: (x + 2) \: ,\: (x - 2)} \\ \\ \\ \bold{Here, \: \: we \: \: can \: \: assume \: \: that}\: \\ \\ \bold{Length \: ,\: l = 3x} \\ \\ \bold{Breadth \: \:, b = x + 2} \\ \\ \bold{Heigth \: \:, h = x - 2}$

_________________________________________

✝$\mathfrak{ \red{THANKS...}}$✝