SOLUTION: The sides of an equilateral triangle measure 16 inches. The midpoints of the sides of the triangle are joined to form another equilateral triangle with sides that are half the leng

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Question 1102350: The sides of an equilateral triangle measure 16 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 triangles are inscribed in the first triangle.
The sum of the perimeters of all four triangles is how many inches?
Answer by greenestamps(13200)   (Show Source): You can put this solution on YOUR website!


As the problem says, when an equilateral triangle is inscribed in another by joining the midpoints of the sides of the first triangle, the side length of the second triangle is half the length of the first.

So the perimeter of the first triangle is 48; that means the second has a perimeter of 24, the third a perimeter of 12, and the fourth a perimeter of 6. The sum fo the perimeters is 48+24+12+6 = 90
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