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

this is under a power-mean inequality topic, so im assuming you might have to use that. guys i really need help 

 Apr 28, 2020
 #1
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I believe that the largest value will occur when a = b.

 

A right triangle with a = b and c the hypotenuse is a 45o - 45o - 90o triangle.

The ratio of the sides of this triangle is sqrt(2) : sqrt(2) : 2

making  (a + b) / 2  =  ( sqrt(2) + sqrt(2) ) / 2  =  2·sqrt(2) / 2  =  sqrt(2) / 1  =  sqrt(2).

 Apr 28, 2020
 #2
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omg thank you!!!

Guest Apr 28, 2020

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