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