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
+23245 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).
