Question 763453


 
The area of a rectangle {{{A=ab}}}, where {{{a}}} and {{{b}}} are sides,
is given by {{{A=12x^2+5x-2}}}
 
given:

one side has length {{{a=4x-1}}}

{{{A=12x^2+5x-2}}}

solution:

{{{ab=12x^2+5x-2}}}.....plug in {{{a=4x-1}}} and solve for {{{b}}}

{{{(4x-1)b=12x^2+5x-2}}}

{{{b=(12x^2+5x-2)/(4x-1)}}}........factor {{{(12x^2+5x-2)}}}: write {{{5x}}} as {{{-3x+8x}}}

{{{b=(12x^2-3x+8x-2)/(4x-1)}}}...group

{{{b=((12x^2-3x)+(8x-2))/(4x-1)}}}

{{{b=(3x(4x-1)+2(4x-1))/(4x-1)}}}

{{{b=((3x+2) (4x-1))/(4x-1)}}}

{{{b=((3x+2) cross((4x-1)))/cross((4x-1))}}}
   
{{{b=3x+2}}}....the length of the other side