let

'a' and 'b be the legs, a>b, a>0, b>0

c = 26 ft the hypotenuse

one leg of a right triangle is 14 ft longer than the other leg

a = b + 14

using the Pythagorean Theorem we have

a^2 + b^2 = c^2

plug a = b + 14 into the last equations

(b + 14)^2 + b^2 = 26^2

by solving we find

b = 10 ft

click here to see the step by step solution of the equation

a = 10 + 14

a = 24 ft

the two other sides of the right triangle are 24 ft and 10 ft.