SOLUTION: please can you help me solve this question,show that if (a,b,c)is a pythagorean triple, then (Ra,Rb,Rc) for any R>0 is also a pythagorean triple. give your geometric interpretation

Algebra ->  Pythagorean-theorem -> SOLUTION: please can you help me solve this question,show that if (a,b,c)is a pythagorean triple, then (Ra,Rb,Rc) for any R>0 is also a pythagorean triple. give your geometric interpretation      Log On


   

Question 1196673: please can you help me solve this question,show that if (a,b,c)is a pythagorean triple, then (Ra,Rb,Rc) for any R>0 is also a pythagorean triple. give your geometric interpretation of this.
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!


We know +c+=+sqrt%28a%5E2+%2B+b%5E2%29+ because of the given information.

Scale (a,b,c) by R:  this results in a triangle with sides (Ra, Rb, Rc).



Now notice  

+sqrt%28%28Ra%29%5E2+%2B+%28Rb%29%5E2%29+ 

= sqrt%28R%5E2a%5E2+%2B+R%5E2b%5E2%29+

= +sqrt%28R%5E2%28a%5E2%2Bb%5E2%29%29+

= R%2Asqrt%28a%5E2+%2B+b%5E2%29+ 

= Rc



The interpretation: scaling a triangle that has sides corresponding to a Pythagorean triple preserves the Pythagorean relationship between the legs and the hypotenuse.