a triangle is made by drawing successive triangle in an equilateral triangle with side 24 cm by joining the mid point of the sides of previous triangle. Find the length of side of nth and 6th triangle. solve with process. Ans is 3/ 2^(n-4) and 0.75 cm.
Answers
Side of an equilateral triangle= 24 cm
The mid-points of its sides are joined to form another triangle whose mid-points are joined to form another triangle. This process continues indefinitely.
Side of 2nd equilateral triangle=12 cm [ Line segment joining mid point of two sides of a triangle is parallel to third side and half of it.]
Similarly , Side of third equilateral triangle=6 cm
......sides are 3, 1.5,3/4,....
Perimeter of 1st triangle=24+24+24=72 cm
Perimeter of 2nd triangle=12+12+12=36 cm
Perimeter of 3rd triangle=6+6+6=18 cm
..........
sum of the perimeter of all the triangles=72+36+18+9+9/2+9/4+........
This is a geometric progression having common ratio =36/72=1/2
Sum of an infinite G.P=
=
= 72 × 2
=144 which is the sum of perimeter of all triangles.