1. A square is drawn inside a right-angled triangle with the two perpendicular sides as 12 cm and 8 cm. what is the side of the largest possible square that can be drawn?
(A) 4 cm (B) 4.8 cm (C) 4.5 cm (D) 4.4 cm (E) 5 cm

• consider the origin as the point of right angle thus (8,0)and (0,12) are the 2 vertices. equation of hypotenuse : 8y+12x=96.
  now solve this with y=x(the diagonal of the largest square)
  x=4.8, y=4.8 .
  hence the answer
• 13 years agoHelpfull: Yes(25) No(6)
• area of triangle is 1/2 * 12 * 8 = 48
  side of square = x
  the entire triangle split into two right angled triangle and one square with dimensions as follows
  i) square with side x
  ii) Right angled triangle with perpendicular sides x and 12-x
  iii) Right angled triangle with perpendicular sides 8-x and x
  
  sum of area of all three = 48
  x^2 + 1/2*x*(12-x) + 1/2*x*(8-x) = 48
  x = 4.8 cm
  
  Ans
  (B) 4.8 cm
• 12 years agoHelpfull: Yes(10) No(2)
• b)4.8cm
  by similar triangles, if the length of the square is x cm,
  ((12-x)/12)=(x/8)
  i.e.,x=4.8cm
• 12 years agoHelpfull: Yes(0) No(3)
• ans = 4cm
  because the one corner of the square should lie at the mid point of the hypotenuous of right angled triangle. and the perpendicular distance from the mid point to any of the two opposite sides is 4cm and if we move that point up or down further then it will form a rectangle. hence largest possible square is of 4cm side.
• 10 years agoHelpfull: Yes(0) No(2)