A square is inscribed in a triangle with side length 10,17 and 21 such that it touches the two side of the triangle and rests on the largest third side.Determine side of such a square.

• let the triangle is ABC,
  a,b,c are sides ; AB=a=17, BC=b=21, CA=c=10
  let the side of square is d
  
  area of triangle= root{s(s-a)(s-b)(s-c)}=84
  
  s=1/2(a+b+c)=48/2=24
  
  area of triangle=1/2*height*base
  1/2*21*height=84
  so height=8
  
  now we will get 2 congruent triangles,
  and the smaller triangle will have
  base= side of square=d, height= height of abc triangle-d=8-d
  
  
  (height of ABC triangle) (height of ABC triangle)
  ------------------------- = -----------------
  (base of ABC triangle) (base of ABC triangle)
  
  8/21=(8-d)/d
  d=168/29.
• 10 years agoHelpfull: Yes(31) No(7)
• let the triangle is ABC,
  a,b,c are sides ; AB=a=17, BC=b=21, CA=c=10
  let the side of square is d
  
  area of triangle= root{s(s-a)(s-b)(s-c)}=84
  
  s=1/2(a+b+c)=48/2=24
  
  area of triangle=1/2*height*base
  1/2*21*height=84
  so height=8
  
  since this height is perpendicular to largest side on which square rests, so side of such square is 8
• 10 years agoHelpfull: Yes(1) No(17)
• @B.Laxmi how can the name of both the triangles be same? may you please clear what is the name of the small triangle ur taking. .
• 10 years agoHelpfull: Yes(0) No(0)