Perimeter, or peRIMeter, means to how far it is
all the way around the RIM.  (You can see the word "RIM"
inside the word "peRIMeter").  If we knew the hypotenuse, c,
we would be able to add the three sides and get the peRIMeter. 

So we use the Pythagorean theorem to find the hypotenuse c:

c2 = a2 + b2

c2 = 52 + 122

c2 = 25 + 144

c2 = 169
     ___
c = Ö169

c = 13

So now we have all three sides:



and we can find the peRIMeter by adding up the three sides:

a + b + c = 5 cm + 12 cm + 13 cm = 30 cm

You were also asked for the area.  A right triangle is one-half
of a rectangle, as we can see from this picture:



The formula for a rectangle is 

Area = base × height

So the area of a triangle, being one-half of a rectangle,

must be

Area =  × base × height

So

Area =  × 5 × 12

Area =  × 60

Area = 30 square cm

Edwin