The area of a rectangular garden is 234 square meters. The width is 4 meters longer than one-half of the length. Find the length and the width of the garden

Divide 234 by 4 = 58.5

W=L/2+4

W = (L+8) / 2

A=LW, using W from above we get:

A=L (L+8) / 2

A = (L^2+8L) / 2, and we are told that A=234 so

(L^2+8L) / 2=234

L^2+8L=468

L^2+8L-468=0

L^2+26L-18L-468=0

L (L+26) - 18 (L+26) = 0

(L-18) (L+26) = 0, since L>0

L=18, and since W = (L+8) / 2

W=13

So the length is 18 meters and the width is 13 meters.