R.M.S>.A.M (you may use the fact)

Algebra Level 3

In a right angled triangle, $A$ and $B$ denote the lenghts of the medians that belong to the legs of the triangle, and the length of the median belonging to the hypotenuse is $C$ . Find the maximum value of the expression $\dfrac{A+B}{C}$ , the answer is of the form $\sqrt{X}$ and so find $X$ .

The answer is 10.

4 solutions

Ayush Garg
May 20, 2015

where did you bring that 5 from ?

avn bha - 6 years ago

Apply Pythagoras in right triangles pqd and triangle fqr

Ayush Garg - 5 years, 11 months ago

Can you show me the value of a, b, and c which satisfy (a + b)/c = sqrt(10) ? I still can't get it

Raden Rifqi Rahman - 3 years, 6 months ago

Take coordinate (a,0), (0,a), (0,0)

sonu gupra - 2 years, 2 months ago

Sahil Sharma
Oct 7, 2017

Consider an isoceles right angled triangle with side as x then find values of A and B for C apply law of cosines .

Deepak Kumar
May 11, 2015

Considerer an isosceles right angled triangle and proceed

but what shall we do if the triangle is not isosceles.for a general triangle how should we proceed with the solution ?

avn bha - 6 years, 1 month ago

Avn Bha
May 10, 2015

please can somebody add a solution to this problem i was not able to solve this .