I need help on this word problem.

Question

A farmer has 120 yards of fencing to build around a rectangular orchard. Let w be the width of the orchard. Write an equation giving the area of the orchard. Find the dimensions of the orchard when the area is 900 square yards.

Answer 1

Perimeter of orchard=2(length+width)=120 yds. So, if L is the length, 2(L+w)=120, L+w=60 and L=60-w. Area=width*length=w(60-w). If area is 900, then w(60-w)=900; w^2-60w+900=0, so (w-30)^2=0 and w=30 and L=30, a square.