Find the value of a, b and c where
a^2+b^2=c^2 and a+b+c=1000

• The property a^2+b^2=c^2 is a Pythagorean triplet of a,b,c. Using the Pythagorean triplet formula, we have
  
  a = m^2 - n^2
  b = 2mn
  c = m^2 + n^2
  
  then, a+b+c = 1000
  or m^2-n^2 +2mn+m^2+n^2 = 1000
  or 2m(m+n) = 1000
  or m(m+n) = 500
  
  Now we list out possible factor pairs of 500. Since, a>0 so m>n . So only possible factor pair satisfying our criteria is (m,m+n) = (20,25).
  Therefore, m=20 and n = 5
  so, a = m^2-n^2 = 375
  b = 2mn = 200
  c = m^2+n^2 = 425
  
• 7 years agoHelpfull: Yes(2) No(0)
• Its better to check out from the options given and just find whether its a pythagorean triplet or not?
• 6 years agoHelpfull: Yes(2) No(2)
• a^2+b^2 = (1000 - (a+b))^2
  a^2+b^2 = 10^6 + (a+b)^2 -2*1000*(a+b)
  ....
• 9 years agoHelpfull: Yes(0) No(5)