Triangles (a,b,c),(m,n,p) and (√(a^2+m^2),√(b^2+n^2),√(c^2+p^2))

 
 
Prove that if   (a, \; b, \; c)   and   (m, \; n, \; p)   are the lengths of the sides of two triangles then

x \; = \; \sqrt { \,(a^2 + m^2) \,},        y \; = \; \sqrt { \,(b^2 + n^2) \,},        z \; = \; \sqrt { \,(c^2 + p^2) \,}

are also the lengths of the sides of some triangle.

 
 
 
 

 
 
 
 
 
 
 
 

 
 
 
 
 
 
 
 
 
 
 
 
 
 

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About benvitalis

math grad - Interest: Number theory
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