Okay, here we have this:
Considering the provided information, we are going to calculate the requested perimeter, so we obtain the following:
According to the given information we know that the jewel has the shape of a right triangle, and we know the two shortest measurements, that is, the legs, therefore to find the hypotenuse we will use the Pythagorean theorem, and we have:

So let's remember that the perimeter is equal to the sum of all the sides of a triangle, therefore we have:
Perimeter=5mm+12mm+13mm
Perimeter=30mm
Finally we obtain that the correct answer is the fourth option.