QUANTITATIVE

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

a. 144 cm

b. 72 cm

c. 536 cm

d. 676 cm

Solution:

The sides of the triangle formed by joining the midpoint of an equilateral triangle is half the side of the equilateral triangle.

Moreover by joining the midpoints of an equilateral triangle we will get another equilateral triangle.

The perimeter of the given equilateral triangle = 3(24)

The perimeter of the second equilateral triangle

=

The perimeter of the third equilateral triangle

=

Proceeding similarly, the sum of the perimeters of all the triangles = 72 + + ..........

= 72 (1 + + ........)

= 72 (

= 72 ´ 2 = 144 cm

Choice (a)