There are an infinite number of triangles with sides 13cm and 17cm. The maximum is close to 30cm when the angle between the two given sides is almost 180 degrees. The cosine rule can be applied x^2=13^2+17^2-2*13*17cos(y) where x is the missing side and y the angle between the known sides. So x=sqrt(458-442cos(y)) where y lies between 0 and 180. The minimum value of x is just greater than 4cm when y is nearly zero, so 17cm would be the longest side. When y=90 degrees, x=21.4cm, the longest side; when y is nearly 180 it's nearly 30cm, as we saw before. When y=67.52 degrees x=17cm and the triangle is isosceles. So x is the longest side when y>67.52 degrees and it can take any value between just over 17cm and just less than 30cm. 17cm is the length of the longest side when y<67.52 degrees.