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One side of an equilateral triangle is 24 cm. The mid points of its sides are joined to form another triangle whose mid points in turn are joined to form still another triangle. The process continues indefinitely. Find the sum of the perimeters of all the triangles.

One side of an equilateral triangle is 24 cm. The mid points of its sides are joined to form another triangle
whose mid points in turn are joined to form still another triangle. The process continues indefinitely. Find
the sum of the perimeters of all the triangles.

Grade:7

5 Answers

bharat bajaj IIT Delhi
askIITians Faculty 122 Points
8 years ago
The side of triangle 1 : 24 cm
The side of triangle formed by joining midpoints : 12 cm
and so onn..
Sum of perimeter - 3(24) + 3(24)/2 + 3(24)/4 + 3(24)/8 .....
= 3(24) [ 1 + 1/2 + 1/4 + 1/8....]
= 3(24)[1/1/2]
=3(2)(24) = 144 cm
Thanks
Bharat Bajaj
IIT Delhi
askiitians faculty
Apptica Corporations
37 Points
8 years ago
The larger triangle will have the perimeter 72 cm. After joining the mid points of the triangle a small triangle also called pedal triangle is formed whose sides are 12 cm and perimeter 36 cm. This process continues to infinite so we have----> Perimeter= 72+36+18+9+............ which forms an infinite Geometric progression with common ratio 1/2. Sum= First Term/(1- common ratio) = 72/(1-0.5) = 144cm
chandramouli
23 Points
8 years ago
144
chandramouli
23 Points
8 years ago
the first triangle we form length of the side become half &it continues so long as we calculate 24(3)+12(3)+6(3)+3(3)+3/2(3)+3/4(3)+..........=144
Sher Mohammad IIT Delhi
askIITians Faculty 174 Points
8 years ago
72+72/2+72/4......
72(1/1-1/2)=144

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