Let the width be w.
The length is 5 yd less than twice the width, so the length is 2w-5.
The area is LW, and the area is 52 yd^2
LW=A
(2w-5)(w)=52
2w^2-5w=52
2w^2-5w-52=0
2w^2 - 13w + 8w - 52 = 0
w(2w - 13) + 4(2w - 13) = 0
(2w - 13)(w + 4) = 0
2w - 13 = 0 or w + 4 = 0
2w = 13 or w = -4
w = 6.5 or w = -4
Since a width cannot be a negative number, discard the solution w = -4.
The width is 6.5 yd.
The length is 2w - 5 = 2(6.5) - 5 = 13 - 8 = 8
The length is 8 yd.
The length is 8 yd, and the width is 6.5 yd.
