Kaylee is painting a design on the floor of a recreation room using equilateral triangles. She begins by painting the outline of Triangle 1 measuring 50 inches on a side. Next, she paints the outline of Triangle 2 inside the first triangle. The side length of Triangle 2 is 80% of the length of Triangle 1. She continues painting triangles inside triangles using the 80% reduction factor. Which triangle will first have a side length of less than 29 inches?
a. Triangle 4
b. Triangle 3
c. Triangle 5
d. Triangle 6
To find the side length of each triangle, we need to multiply the previous side length by 0.8 each time.
Triangle 1 has a side length of 50 inches.
Triangle 2 has a side length of 0.8 * 50 = 40 inches.
Triangle 3 has a side length of 0.8 * 40 = 32 inches.
Triangle 4 has a side length of 0.8 * 32 = 25.6 inches.
Triangle 5 has a side length of 0.8 * 25.6 = 20.48 inches.
Triangle 6 has a side length of 0.8 * 20.48 = 16.384 inches.
Therefore, the first triangle to have a side length of less than 29 inches is Triangle 5.
The answer is:
c. Triangle 5