find the missing segment in the image below

The missing length of the triangle is 22.
It follows from the complete question that the triangle given and the missing length (longest side) can be calculate by means of the proportional as follows;
5/ 15 = 11/ (11+ x)
By cross multiplication;
5 (11 + x ) = 15 (11)
55 + 5x = 165
5x = 165 - 55
5x = 110
x = 22
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