Question

The lengths of the sides of a triangle are 6, 10, and 14. How do you find the perimeter of the triangle formed by joining the midpoints of these sides?

Answer 1

P = 15

Explanation:

I couldn’t find the rule/axiom that relates the interior triangle to the midpoints (it turns out that the lengths are just the same as the half-sides), so I did it the long way by using the Side-Angle-Side (SAS) calculation to find the angles. Using SAS in this situation is trial-and-error.

Plug in the values of the sides and then guess the angle until the result matches the known other side.
SAS: `(((1/2) xx a xx b) xx sin(C)`

In that way I found the angles for each corner (21, 39, 120). Then I used those and the formula again with the half-side values to find the internal triangle side lengths.

Remembering the relationship is much easier, but without a proof it might be harder to justify. With calculated sides of 3, 5, and 7 the perimeter is the sum, 15.