Question

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

• A. $144cm$
• B. $142cm$
• C. $140cm$
• D. $130cm$

Answer 1

The correct option is A $144cm$

From figure, we can observe that the length of the triangle is reducing exactly by $\frac{1}{2}$.
So the sides of equilateral triangle are $24,12,6,\mathrm{3.........}$
Perimeter = $3a$
Sum of Perimeter $=3(24+12+6+\mathrm{3...............})$
$=3\left(24/\right(1-1/2\left)\right)$
$=3\ast 24\ast 2$
$=144$