In the quadrilateral ABCD, ∠BAD = ∠BCD = 90°. If AE = 6 cm, CE = 15 cm and DE = 10 cm, find the length of BF.

1) 9
2) 8
3) 10
4) 15
5) 20

• consider triangle CED,
  tan(angleDCE)=10/15=2/3
  now consider triangle CBF,
  tan(90-angleDCE)=BF/CF => BF=(3/2)*CF -----------1)
  Now consider triangle ADE,
  tan(angle DAE)=10/6=5/3
  consider triangle ABF,
  Tan(90-angleDAE)=BF/AF => BF=(3/5)*AF ----------2)
  equating 1) & 2) , we get AF=(5/2)*CF ----------3)
  But AF+CF=21 => CF=6 cm
  Putting the value of CF in 1) , we get BF= 9 cm
• 10 years agoHelpfull: Yes(1) No(0)