Question 302592
Let's the longest length be "a", the shortest be "c" and the other length be "b" 

the perimeter of a triangle is 90 cm
a + b + c = 90 ... equation 1

Longest side is 6 less than the sum of the measures of the other two sides:
(b + c)-6 = a ... equation 2

Four times the measure of the shortest side equals the sum of the other two sides: 

4c = a + b ... equation 3

Put equation 3 into equation 1:
4c + c = 90 
5c = 90
c = 18 cm

The shortest length is 18cm.