Short Answer (3)
Remark
You should be aware of two facts:
1. Every Pythagorean triple has at least one even number. That's because one of the triples is found from (2xy)^2. 2 xy is even. In this case, you only have 1 even number, so you should focus on it. That number is 40.
2. x should be the bigger numerical value. That's because one of the triples is x^2 - y^2. There is no such thing as a negative distance in plain geometry. Although the negative will disappear when you square it, you should still keep x>y.
Solution
2xy = 40 Divide both sides by 2
xy = 20 By definition you are trying to find whole number results for x and y to equal 20. (You are trying to find integers).
xy = 20
x could be 20
y could be 1
x could be 10
y could be 2
x could be 5
y could be 4
Whatever you choose,
x^2 - y^2 must = 9
x^2 + y^2 must = 41
x = 20
y = 1
x^2 - y^2 = 400 - 1 = 299 That's far too big for this question.
x = 10
y = 2
x^2 - y^2 = 100 - 4 = 96 That's also far to big for this question.
x = 5
y = 4
x^2 - y^2
25 - 16
9 Now that is very encouraging.
x = 5
y = 4
x^2 + y^2 = 25 + 16
x^2 + y^2 = 41 and there's your answer.
