Question

The perimeter of an equilateral triangle measure 48 inches. The midpoints of the sides of the triangle are joined to form another equilateral triangle with sides that are half the length of the outer triangle. This process is continued until three smaller triangles are created within the first triangle.

Use a geometric series to model the perimeters of the four triangles.

The sum of the perimeters of all four triangles is
inches.

Answer 1

Answer:

• Side: 16, 8, 4, 2
• Perimeter: 48, 24, 12, 6
• Sum: 90

Step-by-step explanation:

Side of the first triangle = 48/3 = 16 in

Side of the inner triangles, common ratio is 1/2:

• 16/2 = 8 in
• 8/2 = 4 in
• 4/2 = 2 in

16, 8, 4, 2

Perimeter of the triangles:

• P = 48 in
• P = 8*3 = 24 in
• P = 4*3 = 12 in
• P = 2*3 = 6 in

48, 24, 12, 6

Sum of perimeters:

• 48 + 24 + 12 + 6 = 90 in

Answer 2

Answer:

90 inches

Step-by-step explanation:

first triangle perimeter: 48

cut that in half for the next one: 24

next: 12

final: 6

add all of that together and you get 90