Question

The length l of a rectangle is 4 inches greater than its width w. The area of the rectangle is 252 square inches.Using the method of completing the square, what are the length and width of the rectangle? Show your work.

Answer 1

l=w+4  

lw=252, using l from above

(w+4)w=252

w^2+4w=252,  now halve the linear coefficient, square it, then add that to both sides, ie (4/2)^2=4

w^2+4w+4=256

(w+2)^2=256

w+2=±16

w=-2±16

w=14 or 18, but since w<l

w=14in and l=18in