Answer:
6.9
Explanation:
You want half the side length of an equilateral triangle with an altitude of 12.
Pythagorean theorem
The altitude shown divides the base into equal parts. If one of those parts is x, then the full side length is 2x. The Pythagorean theorem relates the side lengths of the right triangle:
(2x)² = x² +12²
3x² = 144 . . . . . . . . subtract x²
x² = 48 . . . . . . . . divide by 3
x = √48 = 4√3 . . . take the square root
x ≈ 6.9
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Additional comment
You should be familiar with the fact that a 30°-60°-90° triangle has side lengths in the ratio 1 : √3 : 2. This means the shortest side (x) will have a length of 12/√3 ≈ 6.9, since the middle-length side is shown as having a length of 12.