jmc

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.

Accepted Answer

If the side length of each successive equilateral triangle is 150% of the previous triangle, then we can multiply the previous side length by 1.5. We will need to do this three times to get to the fourth triangle, so its side length will be 1.5^3 = 1.5 1.5 1.5 = 3.375 times the original side length. This is the same as 337.5% of the original side length, which represents a 337.5 - 100 = 237.5% increase over the original side length. The perimeter is also a length, so it will be affected in the same way. The percent increase in the perimeter is 237.5%.