Answer:
5√3
Step-by-step explanation:
tan30= 5/z
1/√3= 5/z
z= 5√3
 
        
                    
             
        
        
        
The perimeter of the triangle with those given lengths is 
 
 
        
        
        
G divides each median in the ratio of 2 to 1 (the longer side goes from G to the angle)
triangle AMN is similar to triangle ABC (why?)
AMN is a scaled version of ABC (by a factor of ⅔)
its area should be scaled by (⅔)^2
        
             
        
        
        
5 raised to the 4th power