the perimeter of triangle ABC is 21 units. Give the perimeter of the triangle formed by its midsegments (connecting midpoints of all sides).

Connecting the mid-points of the triangle sides creates a triangle with sides of half the lengths of the given triange making the perimeter 10.5.

Two sides of a triangle ABC have lengths 7cm and 9cm. Which of the following could not be the length of triangle ABC's third side

To find the perimeter of the triangle formed by the midsegments of triangle ABC, we first need to find the midpoints of the sides of triangle ABC.

Given that the perimeter of triangle ABC is 21 units, we can express the lengths of the sides as variables. Let's assume the lengths of the sides are a, b, and c.

The midpoints of the sides of triangle ABC divide each side into two equal lengths. Therefore, the lengths of the midsegments can be expressed as half of the lengths of the corresponding sides. We can represent these lengths as a/2, b/2, and c/2.

The triangle formed by the midsegments is called the midsegment triangle and is similar to the original triangle ABC.

Now, let's find the perimeter of the midsegment triangle.

The midsegment triangle's perimeter is the sum of the lengths of its sides. To find this, we can add the lengths of the midsegments:

Perimeter of the midsegment triangle = (a/2) + (b/2) + (c/2)

Since the midsegments divide the original sides into halves, we can write these lengths as:

Perimeter of the midsegment triangle = (a + b + c)/2

So, the perimeter of the triangle formed by the midsegments is equal to half of the perimeter of the original triangle.

In this case, if the perimeter of triangle ABC is 21 units, the perimeter of the triangle formed by its midsegments is (21/2) = 10.5 units.