What is the largest number of different squares that can be folded out of 180 identical matches

What is the largest number of different squares that can be folded out of 180 identical matches if one match cannot be used to construct two squares and all matches must be used?

Squares are different in size and have no common sides, which means that the squares are separately located and the sides of the first square consist of one match, the sides of the second are of two, the third is of three, etc.
That is, the first consists of 4 matches, the second of 4 * 2 = 8 matches, the third of 4 * 3 = 12 matches.
And this is an arithmetic progression with the first term equal to a1 = 4, the difference d = 4 and the sum S = 180. It is necessary to find n – the number of members of the progression.
According to the formula of arithmetic progression:
S = ((2 * a1 + (n-1) * d) / 2) * n;
180 = ((2 * 4 + (n-1) * 4) / 2) * n;
360 = 4 * n + 4 * n ^ 2;
n ^ 2 + n – 90 = 0.
n = 9.
This means that you can make 9 different squares out of 180 matches.