# The bisector of an equilateral triangle is 9√3. Find its side

July 26, 2021 | education

| In an equilateral triangle, all angles are 60 degrees

The bisector divides the angle in half, we get

Two right triangles

180 – 60 – 30 = 90 degrees

The bisector in an equilateral triangle is the height

One leg of the bisector equals 9√3

Hypotenuse – 2x

The second leg against an angle of 30 degrees is equal to half of the hypotenuse – x

We compose the equation according to the Pythagorean theorem

x * x + 81 * 3 = 4x * x

4x * x – x * x = 243

3x * x = 243

x * x = 243/3 = 81

x = 9

Answer = 9

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