Given a triangle ABC. Find its perimeter if its midline lengths are 5.7 and 9.

It is known from the condition that we are given a triangle ABC. It is also known that the lengths of its middle lines are 5, 7 and 9.

In order to find the perimeter of a triangle, we need to know the lengths of the sides of the triangle.

Let’s remember the triangle centerline theorem. She says that the middle line of the triangle is parallel to one of the sides and is equal to half of it.

That is, in order to find the sides of the triangle, we must multiply the middle lines by 2.

5 * 2 = 10; 7 * 2 = 14; 9 * 2 = 18.

The sides are found, we are looking for the perimeter:

P = a + b + c = 10 + 14 + 18 = 42.