An architect wants to build three similar triangles such that the ratio of the middle triangle. The smallest one has side lengths 5, 12, and 13; the largest triangle has the side lengths 45, 108, and 117. If two of the middle triangle's sides are 39 and 36, what is the length of the third side?

 15

Step-by-step explanation:

small:     5     12      13

middle:  __   36     39

large:    45   108    117

Notice that to get from the small to the large, multiplied by 9

5(9) = 45    12(9) = 108    13(9) = 117

That is because the sides are proportional

To get from small to middle, multiply by 3  

5(3) = 15     12(3) = 36    13(3) = 39

To solve it using proportions: