ADVANCED EXERCISES

(2) A rectangle of 12 cm² area is inscribed in the right triangle with legs of length 6 cm and 8 cm. What are the dimensions of the rectangle?

  

  A = Area of the triangle
  xy = 12

  A = (6)(8)/2 = 24

   (8 - x)y/2 + x(6 - y)/2 = 24 - 12
   (1/2)(8y - xy + 6x - xy) = 12
   8y + 6x - 2xy = 24

   8y + 6x - 2(12) = 24
   8y + 6x = 48

    y = (48 - 6x)/8  =  6 - 3x/4

    x(6 - 3x/4) = 12
    6x - 3x2/4 = 12

    2x - x2/4 = 4
    8x - x2 = 16

    x2 - 8x + 16 = 0
    (x - 4)2 = 0

    x = 4  ==>  y = 3

   The dimensions of the rectangle is 3 cm by 4 cm.