(bonus) a set s of ordered pairs of integers is defined recursively by (1) (1,2) ∈ s and (2,1) ∈ s, and (2) if (m, n) ∈ s, then (m+2,n) ∈ s, and (m, n+2) ∈ s, and (m+1,n+1) ∈ s. there is a simple description of the ordered pairs in s. what is it? your description should be good enough so that you can instantly decide if (12236,912242) is in s.

step-by-step explanation:

assume that you have 3 different side lengths.   apply the pythagorean theorem here:   square each of the two shortest sides; call them a and b, so that their squares are a² and b².   also square the longest side, calling the result c².

now, if a² + b² = c² is true, the triangle is a right triangle; otherwise it is not a right triangle.

perimeter of the base times height

step-by-step explanation: