Question 229271
One side of the rectangular patio is 4 feet longer than the other. If the area of the patio is 140 square feet, what are the dimensions of the patio.


Step 1.  Area A is the width times length for a rectangle.


Step 2.  Let w be the width.


Step 3.  Let w+4 be the length.


Step 4.  Then, A=w(w+4)=140 since area is 140 square feet.


Subtract 140 to both sides to get the following


{{{w^2+4w-140=140-140}}}


{{{w^2+4w-140=0}}}


Step 5.  To solve, use the quadratic formula given as 


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


where a=1, b=4, and c=-140


*[invoke quadratic "x", 1, 4, -140 ]


Selecting the positive answer gives w=10 and w+4=14.  Note the area is 140 square feet using these two dimensions.


Step 6.  ANSWER:  The width is 10 feet and the length is 14 feet.


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