On a test i was given 2 triangles. one triangle gave measurements of all three sides as 2, 4, and 5. the next triangle had sides given 4 and 8 and it asked what the third side should be if the triangles were perpendicular.
how would i solve this? do i find the perimeter of each triangle?

Are you sure the word you're looking for is perpendicular? Perpendicular means at a 90° angle, which in your case, would mean the two triangles would be exactly the same. Did you mean mathematically similar? Because if so, I can tell you that the third side would be 10, using scale factor.

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