Euclid has a triangle in mind. Its longest side has length 20 and another of its sides has length 10.Its area is 80. What is the exact length of its third side?

• The third side will be (2*root 65) units.
• 12 years agoHelpfull: Yes(2) No(0)
• IT can be seen that using Heron' formula will be cumbersome due it calculation involved.
  So, we go thru an alternative solution:
  Assume base AB = 20. So using Area of triangle = 1/2 * base * height (CD) = 80 OR, 1/2 * 20 * H = 80. So. H = 8. Using this AD = 6 (using Pythagoras), and DB = 14. So In triangle CDB, using Pythagoras theorem, CB = sqrt 260.
• 12 years agoHelpfull: Yes(2) No(2)
• As AB=20 area of triangle abc=80 then height will be 1/2*cd*ab=80 so h=cd=8
  now the bd=20-ad
  now use pythagorus theorem in triangle adc
  10^2=h^2+ad^2 so ad=6 therefore value of bd=20-6=14
  again use pythagorus theorem to cal bc so in triangle bdc
  bc^2=bd^2+cd^2
  bc^2=14^2+8^2
  bc^2=260
  bc=sqrt260
• 10 years agoHelpfull: Yes(2) No(1)