The sides of a triangle are 9, 13 and 15. find the length of the longest side of a similar triangle whose shortest side is 7.

Similar triangles share the same 3 angles, and the ratio of each set of corresponding sides is the same in all 3 cases.

The shortest side of the first triangle has length 9, whereas the length of the corresponding side of the 2nd triangle has length 7.

Think:  "the ratio mentioned above is (9/7), or 9:7.

Set up an equation of ratios to find the unknown length of the middle side of the smaller triangle:

9       13
--  =
7         x

Solve this for x.  Perform a similar operation to find the longest side of the 2nd (smaller) triangle.

The solution to the system of equations (-2,2)