Construct an equilateral triangle with altitude is 4.2 cm?

The thing to note here is that the altitude of a equilateral is also the corresponding median and angle bisector. The internal angle is 60 degree hence the angles inside the triangle on either side of the altitude are 30 degree each. Now, here are the steps:

1. Draw a line l and pick any pint D on it.

2. From D draw a perpendicular on the line l. Choose a point A on D such that AD = 4.2 cm (the altitude).

3. From A draw a ray AM such that angle MAD = 30 degree.

4. Extend AM to meet it the line l at point B.

5. Using the compass measure AB and draw an arc from B cutting l at C such that BC = AB. Note that C must be on the same side as D.

6. Join AC.

The triangle ABC is the required equilateral triangle.

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