Answer:
Perimeter of the triangle formed by connecting the midpoint of the triangle [tex]=18\ inches[/tex]
Step-by-step explanation:
Here is an image of the triangles.
The Midpoint Theorem: It states that the segment joining two sides of a triangle at the midpoints of those sides is parallel to the third side and is half the length of the third side.
So we have [tex]\triangle ABC\ and\ \triangle XYZ[/tex].
We see that by applying midpoint theorem.
[tex]XY=\frac{1}{2}\ AC[/tex]
[tex]XZ=\frac{1}{2}\ BC[/tex]
[tex]YZ=\frac{1}{2}\ AB[/tex]
Lets say that [tex]AB+BC+CA =36\inches[/tex]
As perimeter is the summation of the side lengths.
Dividing both sides with [tex]2[/tex]
[tex]\frac{AB+BC+CA}{2} =\frac{36}{2}[/tex]
[tex]\frac{AB}{2} +\frac{BC}{2} +\frac{CA}{2} =18[/tex]
Now replacing [tex]\frac{AB}{2}[/tex] with [tex]YZ[/tex] and following the same for the rest.
We will have: [tex]XY+XZ+YZ=18\inches[/tex].
So the perimeter of the triangles formed by the midpoints of the triangle [tex]18\ inches[/tex]
