Because equilateral triangles are one of the few.... HELP BIG TIME?

Question

because equilateral triangles are one of the few regular polygons that tessellate, you want to cut out different-colored equilateral triangles from construction paper to create a tessellation for the bulliten board. because you no not want to rely on measuring sixty-degree angles, you decide to create a "T" in which each leg of the "T" is the altitude and the top of the "T" is a side of the triangle. You will then connect the end points, as shown below.

[it then shows a picture of a triangle upside down]

If you draw an altitude of length 6 cms, how long to the nearest tenth is each side of the triangle?

choices are

a. 6.9 cm

b. 5.2 cm

c. 6.2 cm

d. 5.9 cm

Answer 1

The altitude is effectively the long side of the triangle that  is the result of bisecting the equilateral.  The hypotenuse of that triangle is the side of the equilateral.  SO... the hypotenuse is 6/cos(30) = 6.938cm.  You work it out from there!