Afield in the shape of a right triangle has an area of 30 square meters. if one leg of the right triangle that forms the field is 4 meters longer than the other leg, what is the length of the longer leg?

Let S=length of shorter leg, then the longer leg measures S+4.
Area of a right triangles = product of legs /2  (in m.)
and
Area of given right-triangle = 30 m^2

To find S, solve
product of legs /2 = S (S+4) / 2 = 30 = area of triangle
S(S+4) = 2*30      [ now distribute ]
S^2+4S = 60        [ subtract 60 from both sides ]
s^2+4S-60=0
Solve for S by factoring
(S+10)(S-6)=0    means  (S+10)=0 or (S-6)=0
Therefore S=6 or S=-10, reject negative root, so
shorter leg = 6m
longer leg = 6m+4m = 10m