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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:12

1 Answers

SHAIK AASIF AHAMED
askIITians Faculty 74 Points
7 years ago
Hello student,
The side of triangle 1 : 24 cm The side of triangle formed by joining midpoints : 12 cm and so on.. 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 and Regards
Shaik Aasif
askIITians faculty

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