The sum of the lengths of the sides of an equilateral triangle___ longer than the sum of the lengths of the?

Question

altitudes of the triangles.


must fill in the blank with must be, may be, or cannot be.

Answer 1

The sum of the sides must be longer than the sum of the sum of the altitudes.

The altitudes bisect the sides of an equilateral triangle, so you have a new triangle inside that is 1 (length of side), 1/2 half (length of bisected side) and (1^2 - .5^2) for the altitude. That's (sqrt3)/2 which is less than 0.9.

If you draw it, it's obvious that the side forms the hypotenuse of the new right triangle, so the side must be longer than the altitude.

And the sum of the sides must be longer than the sum of the altitudes.

Answer 2

must be ex: if the sides are 3 the the altitudes will be 3 also!

Answer 3

MUST BE