The perimeter of a triangle is 117 inches. if one side of the triangle is four more than the shortest side, and the longest side is 11 more than the shortest side, find the lengths of the three sides?

A+b+c=117

lets say that a is shortest and c is longest

1 side is 4 more than shortest
longest is 11 more than shortest
now we know
b=4+a (since longest is 11 more, this cannot be longest)
c=11+a

sub
a+4+a+11+a=117
add like terms
3a+15=117
minus 15 from both sides
3a=102
divide both sides by 3
a=34

find others
b=4+a
b=4+34
b=38

c=11+a
c=11+34
c=45

the legnsh are
34in, 38in, 45in