# The bisector of an equilateral triangle is √3. What is the side?

October 4, 2021 | education

| The bisector of an equilateral triangle is also its height and bisector, then AK = CK = AC / 2, and triangles ABK and CBK are rectangular.

Since ABC is an equilateral triangle, AB = BC = AC.

Let AB = X cm, then AK = AC / 2 = X / 2 cm.

Then, by the Pythagorean theorem, from the right-angled triangle ABK, BK ^ 2 = AB ^ 2 = AK ^ 2.

3 = X ^ 2 – X ^ 2/4.

3 * X ^ 2/4 = 3.

X ^ 2 = 4.

X = 2 cm.

AB = BC = AC = 2 cm.

Answer: The side of the triangle is 2 cm.

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