Use the formulas a=x^2-y^2, b=2xy, c=x^2+y^2 to answer the question. One leg of a triangle has length 11 and all sides are whole numbers. Find the lengths of the other two sides.

Question

The other leg=

the hypotenuse =

Answer 1

1. So, are the three sides defined aby lengths a, b, c with x and y just arbitrary variables, or by xy coordinates of the three corners, with a, b and c just arbitrary variables?
2. Is this a right triangle -- that infor is later and not as bold!

1. If x is 2 and y is 1, you get the classic 3-4-5 right triangle sacred to Egyptians, but no 11.
2. 11 cannot be b as it is even and a whole number.
3. If c is 11, you have an impossible time finding two small squares that add up to that!
4. If a is 11, 36 - 25 works, so x=6, y=5, b=60, c=61.

Not my idea of a learning tool, in a strict algebra or geometry space, as much as a groping challenge, but then much of life is like that!