Question

An equilateral triangle has sides of length 2 units. A second equilateral triangle is formed having sides that are 150% of the length of the sides of the first triangle. A third equilateral triangle is formed having sides that are 150% of the length of the sides of the second triangle. The process is continued until four equilateral triangles exist. What will be the percent increase in the perimeter from the first triangle to the fourth triangle? Express your answer to the nearest tenth.

Answer 1

Answer:

The percent increase in the perimeter is 337.5%

Step-by-step explanation:

The easiest way to approach this problem is by using consecutively the simple rule of three.

If the first triangle has sides of length two then, we can compute the second triangle's sides length as follows:

2 units------100%

X units------150%    

this way

$X = 2*\frac{150}{100}\\ X =2*1.5\\X=3units$.

Now for the third triangle we repeat the same process

3 units------100%

X units------150%  

getting that the length of the sides for the third triangle is

$X = 3*\frac{150}{100}\\ X =3*1.5\\X=4.5units$.

Now for the last triangle we repeat the same process

4.5 units------100%

X units------150%  

getting that the length of the sides for the last triangle is

$X = 4.5*\frac{150}{100}\\ X =4.5*1.5\\X=6.75units$.

Now, we need to know the perimeter of the first and last triangle. This can be calculated as the sum of the length of the sides of the triangle.

For the first triangle

$P_{first}=2+2+2\\P_{first}=6$

and for the last triangle

$P_{first}=6.75+6.75+6.75\\P_{first}=20.25$.

To compute the percent increase in the perimeter from the first to the fourth triangle we will use one last simple rule of three (this time the percentage will be the variable)

6 units------100%

20.25 units------X%

so

$X = 100\frac{20.25}{6}\\ X=337.5\%$.