Question

solve the above problem

Answer 1

AM AND CN ARE THE MEDIANS OF

BC AND AB

SO

AN=BN = 1/2 AB

BM=MC = 1/2BC

for the triangle ABC

Ac² = BC² + AB²---------------(1)

FOR TRIANGLE BNC

NC² = BC² + BN²

=>NC² = BC² + 1/4 AB²

[SINCE BN=1/2AB]

=> 4CN² = 4BC²+AB²-------------(2)

[MULTIPLYING BOTH SIDES BY 4]

FOR TRIANGLE ABM

=>AM²= AB² + BM²

=>AM² = AB² + 1/4BC²

=>4AM² = 4AB² + BC²---------------(3)

(2)+(3)

=>4(AM²+CN²)= 5(AB² + BC²)

=> 4(AM² + CN²) = 5 AC²(FROM 1)