ABC is an isosceles triangle with AB=AC and BC=48. DEFG is a square inscribed in triangle ABC such that vertices D and E lie on AB and AC respectively, while vertices F and G lie on BC. If [ADE]=24, what is the side length of the square DEFG?

• Draw prependicular from A to AC meeting BC at M and DE at L.
  Triangles ALE and AMC are similar. DL=LE= 1/2 of side of square
  MC= 48/2=24 as ABC is isosceles triangle.
  If side of square is 2x, then LE=x and AL= 2*24/x= 48/x, AM= ax+48/x
  
  now
  AL/AM = LE/MC = x/24
  putting values and solving for x,
  we get
  x= 6 units
  side of square = 2x=2*6=12 units
• 12 years agoHelpfull: Yes(4) No(0)
• side of ADC is 10,8,6 (area is 24) now DE= 12 (AO is perpendicular to DE )
  hence DE(Sides of Square)= 2*DO = 2*6=12 Ans
• 12 years agoHelpfull: Yes(2) No(1)
• is 12 the right answer ?
  
• 12 years agoHelpfull: Yes(1) No(1)