1) 3628799 (Online source)
2) (2008 AMC 10A)
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
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,
Substituting (4) into (3),
Therefore, the length of the hypotenuse is .