One side of an equilateral triangle is 36 cm. The mid points of i

SOLUTION

Given, one side of the equilateral triangle is 36 cm.

Now, the triangle formed on joining the mid points will be another equilateral triangle with sides equal to half the side of the equilateral triangle and so on.

Thus, an infinite G.P. will be obtained if we add their perimeters

Perimeter of an equilateral triangle = 3 × side

∴ Sum of perimeters = 3 × 36 + 3 × 18 + 3 × 9 + …………

⇒ Sum of perimeters = 3 × 36(1 + ½ + ¼ ….. )

Thus it is an infinite G.P. with ratio ½.

Sum of an infinite G.P. \(= \frac{a}{{1 - r}}\) 

⇒ Sum of perimeters \(= 3 \times 36 \times \frac{1}{{1 - \frac{1}{2}}}\)

⇒ Sum of perimeters = 108 × 2 = 216 cm