Question

6) If the perimeter of the equilateral triangle ABC is x inches. The mid points of the sides are joined to form the smaller triangle and

the process goes on as in the diagram. If the perimeter of the 6th triangle is 3 inches, find the value of x.

​

Answer 1

96 in

Explanation:

If the midpoints of the sides are joined to form the smaller triangle, then the perimeter of the smaller triangle is half the perimeter of the greater triangle, because the sides of the smaller triangle are midlines of the greater triangle. By the triangle's midline theorem, each triangle's midline is half the side to which this midline is parallel.

So, if the perimeter of 6th triangle is 3 inches, then the perimeter of 5th triangle is 6 inches, the perimeter of 4th triangle is 12 inches, the perimeter of 3rd triangle is 24 in, the perimeter of 2nd triangle is 48 in and the perimeter of the initial triangle is 96 in