Four lines parallel to the base of a triangle divide each of the other sides into five equal segments and the area into five distinct parts. If the area of the largest of these parts is 27, then what is the area of the original triangle?

1) 135
2) 175
3) 75
4) 225

• dekho ans yahi h pata nahi kase aya 75
• 8 years agoHelpfull: Yes(0) No(1)
• section plus everything above that section base is a triangle.
  They are all similar triangles with the side lengths in the proportion
  The length of base and height are also in the same proportion, of course.
  So, the areas are in the proportion
  1:2:3:4:5
  The area of the triangle made up of the top two sections is 4 times the area of the smallest (top) triangle.
  The area of the triangle made up of the top three sections is 9 times the area of the smallest (top) triangle.
  The area of the triangle made up of the top four sections is 16 times the area of the smallest (top) triangle.
  The area of the triangle made up of the top five sections is 25 times the area of the smallest (top) triangle.
  
  
  Let's call the area of the smallest (top) triangle x square centimeters.
  The area of the triangle made up of the top four sections is 16x square centimeters.
  The original triangle's area is 25x square centimeters.
  The difference, 25x-16x=9x , is the area, in square centimeters of the bottom section.
  Our equation is 9x=27 x=3.
  The area of the original triangle is
  25x square centimeters.
  =75 ........................... ANSWER............
• 8 years agoHelpfull: Yes(0) No(0)