Question

HELP PLEASE!!! 10 PTS BRAINLIEST!!!

Answer 1

Answer:

Perimeter of the triangle formed by connecting the midpoint of the triangle $=18\ inches$

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 $\triangle ABC\ and\ \triangle XYZ$.

We see that by applying midpoint theorem.

$XY=\frac{1}{2}\ AC$

$XZ=\frac{1}{2}\ BC$

$YZ=\frac{1}{2}\ AB$

Lets say that $AB+BC+CA =36\inches$

As perimeter is the summation of the side lengths.

Dividing both sides with $2$

$\frac{AB+BC+CA}{2} =\frac{36}{2}$

$\frac{AB}{2} +\frac{BC}{2} +\frac{CA}{2} =18$

Now replacing $\frac{AB}{2}$ with $YZ$ and following the same for the rest.

We will have: $XY+XZ+YZ=18\inches$.

So the perimeter of the triangles formed by the midpoints of the triangle $18\ inches$