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Answer for wk 3:

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 .


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