A square of the longest possible side is drawn inside the triangle ABC with one side of the square lying on side BC. If AB = 13, BC = 21 and AC = 20, find the side of the square.
A.84/11
B.7
C.28/3
D.31/4

• A. 84/11
  
  s=(13+21+20)/2 = 27
  
  Area of triangle(A)= [27*(27-13)*(27-21)*(27-20)]^(.5) = 126
  
  height of triangle(h)= 2*A / base = 2*126/21 = 12
  
  from, similarity of triangles
  
  h/(h-x) = BC / x where x is side of square
  => 12/(12-x) = 21/x
  => x = 84/11
  
  
• 9 years agoHelpfull: Yes(55) No(1)
• a Square contain equal length of side,there is no longest size or shortest size.
  he give square side BC=21,this is length of all sides
• 9 years agoHelpfull: Yes(1) No(11)
• DEFG SQUARE
  
  triangle ABC and triangle ADE
• 9 years agoHelpfull: Yes(1) No(1)
• Let P and Q are the vertices of the square on AB and AC respectively and R and S on side BC.
  s=(13+21+20)/2 = 27
  
  Area of triangle(A)= [27*(27-13)*(27-21)*(27-20)]^(.5) = 126
  
  height of triangle(h)= 2*A / base = 2*126/21 = 12
  now from, similarity of triangles APQ and ABC
  12-X/21=X/12
  X=48/11
  
  
• 8 years agoHelpfull: Yes(1) No(1)
• @ rakesh
  kindly explain h/(h-x) = BC / x where x is side of square,
  which 2 triangles you have taken as similar..
• 9 years agoHelpfull: Yes(0) No(3)