Question 848194
Let a,b be the short sides  let c be the longest side. We know that a=2/3 c and b = 2/3 c from "Each of the two smaller sides are 2/3 the length of the longer side"

a+b+c = 186

(2/3)c + (2/3)c + c = 186

7/3 c = 186

c = 186 * (3/7)

c = 558/7

a = b = 2/3 * c  = 2/3 * 558/7 = 372/7

This means a = 372/7 , b = 372/7, c = 558/7