A right triangle has legs \(a\) and \(b\) and hypotenuse \(c\) Find the largest possible value of \(\dfrac{a+b}{c}\)

all i know is c will always be bigger than a or b, but a+b will always be bigger than c.

If you are allowed an "isosceles right triangle", you would have a=1 and b=1 and c=sqrt(2).

So: (a + b) / c = (1 + 1) / sqrt(2) =1.4142.......etc. This gives you the largest value possible, I think!.