if 2m=200cm3m=300cm,then prove that 5m=500cm using an euclid's axiom.

Answer :

Given 

2m  =  200 cm                    -------------- ( 1 )
And

3m  =  300  cm                   -------------- ( 2 )

Now we apply Second axiom of Euclid , that states that " ​If equals be added to equals, then the wholes are equal. "

So we add equation 1 and 2 and get 

2m  +   3m   =  200 cm   +   300 cm 

5m   =  500 cm                                                     ( Hence proved )