Chapter 11.3, Problem 60PPS

To determine

Find the sum of the perimeter of the first eight triangles.

Answer to Problem 60PPS

Total Perimeter of 8 such Equilateral Triangle is 119.5 cm

Explanation of Solution

Given:

The figure:

  

In the figure, the sides of each equilateral triangle are twice the size of the sides of its inscribed triangle. If the pattern continues, find the sum of the perimeter of the first eight triangles.

Concept Used:

Perimeter of the big Equilateral Triangle = 3 times its sides

Calculation:

Side of big Equilateral Triangle = 20 cm

Perimeter of the big Equilateral Triangle = $3·\text{side}=3·20=60\text{cm}$

  $a_1=60\text{cm};r=0.5\text{cm};n=8,\text{find}{\text{S}}_8$

Total Perimeter of 8 such Equilateral Triangle is:

  $\begin{array}{l}{a}_1=60\text{cm};r=0.5\text{cm};n=8,\text{find}{\text{S}}_8\\ {\text{S}}_{\text{n}}=\frac{a_1(1-r^n)}{1-r}\\ {\text{S}}_8=\frac{60(1-{0.5}^8)}{1-0.5}=\frac{59.765625}{0.5}\approx 119.5\end{array}$

Thus, Total Perimeter of 8 such Equilateral Triangle is 119.5 cm