A triangle having sides 10, 17 , 21 . A square is placed inside the triangle touching two sides and lie on the largest side of a triangle. Find the length of square?

• m sry answer is 168/29......apply Heron's formula get the area ,equate the area with 0.5*b*h to get h (altitude),h=8, and then by basic proportionality theorem we get length of the square= 168/29.
• 11 years agoHelpfull: Yes(10) No(2)
• length of square is 168/29 units
  
  let us consider a triangle abc with ab = 10, bc=21 and ac =17
  let square be pqrs with points p on ab, q and r on bc and s on ac
  let each side of square is x. we have to find x
  now for this we apply cosine formula in triangle abc to get angle b and c
  cos(ang b)= 0.6
  cos(ang c)= 15/17
  
  now we see smaller triangles pbq and src
  in triangle pbq
  cos(ang b) = 0.6 so sin(ang b) = 0.8
  tan (ang b)= 4/3 = pq/qb
  pq=x
  so x/qb = 4/3
  qb = 3/4x
  
  now seeing in triangle src
  cos(ang c)= 15/17
  tan(ang c)= 8/15
  sr/rc = tan(ang c) =8/15
  sr = x
  
  
  now bc=21 = qb+qr+rc
  qr=x (as it is side of square)
  qb= 3/4x
  rc = bc-(qr+qb) = 21-7/4x
  
  now sr/rc=8/15
  x/(21-7/4x) = 8/15
  solving we get x = 168/29
  
• 11 years agoHelpfull: Yes(4) No(1)
• awesome problem... see this it will help http://www.qbyte.org/puzzles/p076s.html
  
• 11 years agoHelpfull: Yes(4) No(0)
• base of triangle=b=21 and height=h,square side=x.
  find area by heron's formula and equate it to 0.5*b*h..get the h
  The area of the whole triangle is b*h/2.
  The area of the small triangle on the top is x*(h-x)/2
  The area of the square is x^2.
  The area of the triangle that is obtained by sliding together the two smaller triangles standing on the base is (b-x)*x/2.
  So
  x = b*h/(b + h).
  
  
  
• 11 years agoHelpfull: Yes(3) No(0)
• Ans -> 5.6
  -> base of triangle=b=21 and height=h,square side=a.
  -> find area by heron's formula(=84)and equate it to 0.5*b*h..get the h = 8.
  -> The area of the whole triangle =(The area of the small triangle on the top) + (The area of the triangle that is obtained by sliding together the two smaller triangles standing on the base) + area of square
  =>84 = [a*(h-a)/2] + [(b-a)*a/2] + a^2.
  =>84 = [a*(8-a)/2] + [(21-a)*a/2] + a^2.
  =>solving, a = 5.6
  
  
• 11 years agoHelpfull: Yes(2) No(0)
• length of square would be 7 units.
• 11 years agoHelpfull: Yes(1) No(12)
• Asan question hai,, but i passed it. Due to lack of time.
• 11 years agoHelpfull: Yes(0) No(27)
• http://www.qbyte.org/puzzles/p076s.html
• 11 years agoHelpfull: Yes(0) No(0)