A field 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