SOLUTION: Hello! I will paste the problem below. I do not know what the question means by choosing two values that are greater than 10 that can be written in their exact form. What is exact

Algebra ->  Triangles -> SOLUTION: Hello! I will paste the problem below. I do not know what the question means by choosing two values that are greater than 10 that can be written in their exact form. What is exact       Log On


   



Question 1179290: Hello! I will paste the problem below. I do not know what the question means by choosing two values that are greater than 10 that can be written in their exact form. What is exact form? I'm struggling to come up with these two values, any help would be appreciated.
"Choose a and b so that each is greater than 10 and so that they could be the legs of a 'special' right triangle written in their exact form."

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
you actualy need one of pythagorean triples
Pythagorean Triples if it satisfies the equation,
a%5E2%2Bb%5E2=c%5E2
List of Primitive Pythagorean Triples:
(3,+4, 5)
(5,12, 13)
(7, 24, 25)
(8, 15, 17)
(9, 40,+41)
(11, 60, 61)=> first one that you can use, or one of the following triples
(12, 35,+37)
(13,+84,+85)
so, let a=12 and b=35 ( each is greater than 10)
then plug it in
a%5E2%2Bb%5E2=c%5E2
12%5E2%2B35%5E2=c%5E2
1369=c%5E2
c=sqrt%281369%29
c=37
it confirms we have triples (12, 35,+37)