Question 1187292


the length {{{L}}} of rectangle piece of cardboard is {{{5cm}}}} longer than it is wide,
{{{L=W+5}}}

after cutting {{{3cm}}} (which will be the height of the box) square out of each corner, 

{{{L=W+5-6}}}->{{{L=W-1}}}
{{{W-6}}}

the height {{{h=3}}}

Then the four flaps are folded up to form a box without a lid. 

The volume of this box is {{{V=450cm^3}}}. 

{{{LWh=450cm^3}}}

{{{(W-1)(W-6)*3=450}}}

{{{3W^2 - 21 W + 18=450}}}

{{{3W^2 - 21 W + 18-450=0}}}

{{{3W^2 - 21 W -432=0}}}

{{{W^2 - 7W -144=0}}}......using quadratic formula we get

{{{W = -9}}}
{{{W =16}}}-> we need positive value for the width

then
{{{L=16+5}}}
{{{L=21}}}

the length and width of the original piece of cardboard are {{{ 21cm}}} and {{{16cm}}} respectively 

proof:

{{{(21-6)*(16-6)*3=450}}}
{{{450=450}}}