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

 Apr 15, 2020
 #1
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all i know is c will always be bigger than a or b, but a+b will always be bigger than c.

 Apr 15, 2020
 #2
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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!.

 Apr 15, 2020

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