Determine the scaling of the perimeter of the triangle to the ratio of the sides of the triangles. The scale for each side is the fraction of one number of the ratio over the sum of the three numbers in the ratio. For instance, if the ratio of a random triangle's sides are three to two to one, the scales for each side would be one over six because three plus two plus one is six and a number in the ratio is one, two over six or one-third, and three over six or one-half.
Multiply each scale to the perimeter to find the lengths of each side. For example, if the perimeter of the triangle is 36, the lengths of the triangle are six because 36 multiplied by one over six is six, 12 and 18. Notice that the sum of all three sides equals 36, the given perimeter.
Determine which of the three lengths is the longest. This length is the hypotenuse of the triangle. If the three lengths of the triangle are six, 12 and 18, the hypotenuse of the triangle is 18.