One side of triangle is half the longest side. the third side is
10
10 feet less than the longest side. the perimeter is
75
75. find all three sides.

Let S be the first side. 
Longest side is then 2S.
Third side is 2S-10.
Perimeter is sum of all three sides = S+2S+2S-10 = 75
=>
5S-10=75
5S=75+10=85
S=17

Therefore
S=17 is the first side. 
Longest side is then 2S=2*17=34.
Third side is 2S-10=2*17-10=24.