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

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.