Question 69253
I WOULD SAY THAT YOU ARE RIGHT ON THE MONEY ON THIS PROBLEM.  GOOD WORK!!!!


Let x= the width of the rectangle
Then 2x+4=length of rectangle (4 cm more than twice the width)

Area of rectangle =l*w=(2x+4)(x) so our equation to solve is:

{{{(2x+4)(x)=74}}}  get rid of parens

{{{2x^2+4x=74}}}  subtract 74 from both sides


{{{2x^2+4x-74=0}}}  divide both sides by 2

{{{x^2+2x-37=0}}}  quadratic in standard form

We'll solve using the quadratic formula:

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

{{{x = (-2 +- sqrt( 2^2-4*(-37) ))/(2) }}} 

{{{x = (-2 +- sqrt(152 ))/(2) }}} 

{{{x = (-2 +- sqrt(152 ))/(2) }}} 

{{{x = (-2 +-12.330 ))/(2) }}} 

{{{x = (-2 +12.330 ))/(2) }}}
{{{x = (10.330 ))/(2) }}}
{{{x=5.165}}} cm -----------------width of rectangle

{{{2x+4=2*5.165+4=14.330}}} cm---------------length of rectangle

We'll discount the negative value for x

CK

Area = l*w=14.330*5.165=74.01~74 ---ok

Hope this helps----ptaylor