Question

One side of an equilateral triangle is 18 cm. The

mid points in turn are joined to form still another

triangle. The process is continued indefinitely find

sum of perimeters of all triangles. (in cm)​

Answer 1

Your Question:-

⇒ One side of an equilateral triangle is 18 cm.

The mid points in turn are joined to form still another  triangle.

The process is continued indefinitely find  sum of perimeters of all triangles. (in cm)​ ?

Your Answer :-

⇒ According to the mid point theorem :-

The sides of each triangle formed by joining the midpoint of an equilateral triangle are half of the sides of the equiletere triangle .

∴ Sum of the perimeter of all the triangle are :-

⇒ $P = 3*18 + 3*9 + 3*4.5 + 3*2.25.........\infty}$

⇒ $P = 3*( 18+ 9 + 4.5 + 2.25 + .......\infty}$

its a G.P.

where :-

a = 18

r = $\frac{1}{2}$

∴ $P = 3*(\frac{18}{1-\frac{1}{2} } )$

⇒ P = 3*36

⇒ P = 108 cm

it is your answer:- 108 cm

hence the sum of all the triangle is 180 cm.

Thank you......