Similar polygons have the same shape, but not necessarily the same size. Are rectangles with dimensions 8 x 5 and 25 x 40 similar?

Two triangles have integral side lengths, with all sides being less than 50. They are similar but not congruent, and the smaller triangle has two side lengths identical with the larger triangle.

What is the sum of the side lengths of the larger triangle?

Assume that both the pizzas fit perfectly inside their respective boxes.

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