A rectangular sign must have an area of44 square yards Its l

A rectangular sign must have an area of44 square yards. Its length must be 4 yards more than its width. Find the dimensions of the sign. Key: (2+43) yd by (-2+43) yd PLEASE EXPLAIN THANK YOU.

Solution

Let the length of the rectangular sign be x yards. Then its width is x-4 yards, so that its area is length*width = x(x-4) = x² -4x. Thus,  x² -4x = 44 or, x² -4x-44 = 0. On using the quadratic formula, we have x = [4 ± { (-4)² -4*1*(-44)}]/2*1 = [4 ± ( 16+176)]/2 = (4 ± 192)/2 = ( 4± 412)/2 = 2± 212 = 2 ± 43 . Since x cannot be negative, we have x = 2 + 43 . Thus, the length of the rectangular sign is 2 + 43 yards. Then its width is 2 + 43 -4 = - 2 + 43 yards.