An equilateral triangle has side lengths of 10. If the consecutive midpoints of the triangle are joined, then find the perimeter of the new triangle that is formed
naturally, if the midpoints are joined, the new sides are 1/2 as long as the original sides.
p =15
To find the perimeter of the new triangle formed by joining the consecutive midpoints of an equilateral triangle, we need to first find the length of the sides of the new triangle.
In an equilateral triangle, all three sides have the same length. Let's call this length 's'. In this case, the given side length of the equilateral triangle is 10.
To find the length of the sides of the new triangle, we need to find the length of the line segment that joins the midpoint of one side to the midpoint of the adjacent side.
In an equilateral triangle, the line segment joining the midpoint of one side to the midpoint of the adjacent side is half the length of the side.
So, the length of the sides of the new triangle formed can be found using the formula:
New triangle side length = (1/2) * Side length
Substituting the given side length, we get:
New triangle side length = (1/2) * 10 = 5
Since the new triangle is also equilateral, all three sides have the same length of 5.
The perimeter of the new triangle can be found by adding up all the lengths of its three sides:
Perimeter of new triangle = 5 + 5 + 5 = 15
Therefore, the perimeter of the new triangle formed by joining the consecutive midpoints of the equilateral triangle with side lengths of 10 is 15 units.