The way I know is because I memorized every square up to 33.
BUT that's probably not helpful to you.
Remember that every perfect square has an odd number of factors. I'm not going to list them all out, but the factors of 35 are 1, 5, 7, and 35, giving it an even number of factors. All the rest have an odd number of factors because of the property of a perfect square: a number times itself gives a perfect square, but that number only counts as 1 factor.
To find the perimeter of the triangle we need to add all the sides. Since the sides all have different denominators in their fractions, first we need to make the denominator the same.
5/4 = 10/8
3/2 = 12/8
1/8 = 1/8
Then we just add the numerators and keep the denominator the same, which gets us 23/8 meters. Since 23/8 can be simplified, that's the answer.