Triangle spiral

Geometry Level 3

A spiral of similar triangles like the one depicted above is constructed such that the smallest triangle (the one with the least perimeter) has a base of 4 and height of 3.

If the length of the 9th triangle's hypotenuse can be represented as \(\frac{a}{b}\) for positive co-prime integers a,b, find a+b.

Use of a calculator is expected.

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