1) 3628799 (Online source)

2) (2008 AMC 10A)

**Solution (1):**

We try to derive a general formula for . We can see that

, for every .

Don't ask me how I get this -- you have to practice lots of problems to see the pattern. Thus, applying the formula, we get

**Solution (2):
**At first glance, this problem seems hard to solve because it only gives us the perimeter and area. However, notice that it is a

**right triangle**. This inspires us to set the legs of triangle as a,b, and its hypotenuse as . Thus, we arrive at the simultaneous equations:

Simplifying the first equation gives us:

From here we can see that it is impossible to find the value of a,b respectively. Hence, we change our approach -- we find a+b and subtract it from the perimeter of the triangle, which is given, to obtain the hypotenuse. Therefore,

From (2),

Substituting (4) into (3),

Therefore, the length of the hypotenuse is .