Question 912108

When the width is {{{W= (n+2) }}} the height (or length) is {{{3}}} less than {{{W=(n+2)}}}, the {{{L=W-3= (n+2)-3}}}

 and the area is {{{A=119}}} 

solution:

{{{A=L*W}}} 

{{{A=((n+2)-3)*(n+2)}}} 


{{{119=(n+2-3)*(n+2)}}} ...solve for {{{n}}}

{{{119=(n-1)*(n+2)}}}

{{{119=n^2+2n-n-2}}}

{{{0=n^2+n-2-119}}}

{{{n^2+n-121=0}}}


{{{n = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} 


{{{n = (-1 +- sqrt( 1^2-4*1*(-121) ))/(2*1) }}} 

{{{n = (-1 +- sqrt( 1+484))/2 }}}
 
{{{n = (-1 +- sqrt( 485))/2 }}} 

{{{n = (-1 +- 22.02271554554524 )/2 }}} 


solutions:

{{{n = (-1 + 22.02271554554524 )/2 }}} 

{{{n=21.02271554554524/2}}}

{{{n=10.51135777277262}}} ....since we dealing with width and length, we need only positive solution 



the width: {{{W=(n+2)}}} => {{{W=(10.51135777277262+2)}}} =>{{{W=12.51135777277262}}} 

the length: {{{L=W-3= 12.51135777277262-3}}} => {{{L= 9.51135777277262}}} 

{{{A=L*W}}} => {{{119=9.51135777277262*12.51135777277262}}} =>{{{119=119}}}