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Construct an equilateral triangle if its altitude is 6 cm.

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Steps of Construction 

(i) Draw a line XY.

(ii) Construct perpendicular PD at any point D on the line XY.

(iii) From point D, cut-off line segment AD = 6 cm. 

(iv) Construct ∠BAD = ∠CAD = 30°. Then ABC is the required triangle.

 Justification 

 As ∠A = ∠BAD + ∠CAD = 30 °+ 30° = 60° and AD perpendicular BC therefore, △ABC is an equilateral triangle with altitude AD = 6 cm. 

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