Question

The midpoint of the sides of triangle ABC are labeled D, E, and F. If the perimeter of triangle DEF is 24 find the perimeter of triangle ABC.
A.48
B.72
C.96
D.120

Answer 1

Ok well the only thing that makes since to me is that the triangle is a Equilateral Triangle, so all the sides are going to be the same. And if the perimeter is 24, then you divide that by 3, and you get 8. And if DEF is the midpoints of triangle ABC, then DEF is an upside down triangle in the triangle ABC. So all the sides of ABC are double whatever DEFs are. And DEFs were 8, so 8 times 2 is 16. And to get the perimeter you add that together 3 times and you get 48. So i'm not sure exactly how you would do this, but i'm pretty sure this is the way. If not i'm sorry i couldn't help. :(

Answer 2

Linking the midpoints of each side of a triangle cuts it into four smaller, mathematically similar versions of itself, the central of which is reflected vertically - ALWAYS. Therefore, the area scale factor of the new, smaller triangle to the original larger triangle, is 4. $\sqrt{4}$ would give the linear scale factor (the nth route of the area scale factor, where n is the dimension of operation), which is 2.
The original triangle must have a perimeter twice as long as the smaller triangle.
A - 48$\sqrt{4}$