For a trapezium, S1 denotes the sum of the squares of the sides and S2 denotes the sum of the squares of the diagonals. S1 - S2 = 576. If the longer parallel side is 50 cm, the shorter parallel side is ?

1) 26
2) 22
3) 18
4) 30

• my take on this problem is as follows i am solving according to the dia attached
  
  now it is given sum of squares of sides - sum of squares of diagonals=576
  
  sum of squares of sides s1= AB^2+bc^2+cd^2+da^2
  
  sum of squares of diagonals is s2=AC^2+bd^2
  
  
  now there is a formula AC^2+BD^2= Ad^2+bc^2+2abcd
  
  
  AB^2+bc^2+cd^2+da^2-(Ad^2+bc^2+2abcd)=576
  
  ab^2+cd^2-2abcd=576
  
  subs ab=50
  
  we can form quad equation of
  
  cd^2-100cd+1924=0
  
  
  solving we get 74 and 26
  
  the longer side is 74
  
  
  hope it's clear
• 11 years agoHelpfull: Yes(0) No(0)