48 cm
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With sides of 5 and 12, you can make a triangle with any perimeter you want between 24 and 34. If you call them "legs" because they are the sides of a right triangle, then the hypotenuse is 13, and the perimeter is 30.
It really depends on what your hypothesis is! But I expect a hypotenuse could be more useful in this context. However, knowledge of the hypothesis, hypotenuse even, is not enough to enable you to find the perimeter.
It is: perimeter minus hypotenus+base = height Area = 0.5*base*height
The perimeter is equal to the sum of (leg-1) plus (leg-2) plus (hypotenuse).
It is impossible. You need another measurement, such as angle, side length or area etc.