Question 221567
The length of a rectangle is 12 meters longer than half the width.  The area of the rectangle is 90 square meters.  Find the dimensions of the rectangle.


Step 1.  Let w be the width.


Step 2.  Let {{{w/2+12}}} be the length.


Step 3.  Area {{{A=w(w/2+12)=90}}}


Step 4.  Solving A in Step 3 yields the following steps.


{{{w^2/2 +12w=90}}}


Multiply 2 to both sides to get rid of denominator


{{{2w^2/2+2*12w=90*2}}}


{{{w^2+24w=180}}}


Subtract 180 from both sides to get a quadratic equation


{{{w^2+24w-180=180-180}}}


{{{w^2+24w-180=0}}}


Step 5.  To solve equation in Step 5, use the quadratic formula given below


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


where a=1, b=24, and c=-180


*[invoke quadratic "w", 1, 24, -180 ]


With {{{w=6}}}, then {{{w/2+12=15}}}.  Area A=6*15=90 which is a true statement.


Step 6.  ANSWER:  The dimensions of a rectangle are 6 meters and 15 meters.


I hope the above steps were helpful.


For FREE Step-By-Step videos in Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


Good luck in your studies!


Respectfully,
Dr J