Question
Fri March 06, 2015 By: Akansha Banerjee

Construct an equilateral triangle whose altitude is 4.5cm.

Expert Reply
Mili Hariyani
Sat March 07, 2015

Draw a line PQ.

Take any point L on this line.

Construct perpendicular AL on PQ.

Cut a line segment AD from D equal to 4.5 cm.

Make angles equal to 30° at A on both sides of AD, say ∠CAD and ∠BAD where B and C lie on XY.

Then, ABC is the required triangle.

Justification:

Since ∠A = 30° + 30° = 60° and AL ⊥ BC,

Therefore, ∆ABC is an equilateral triangle with altitude AL = 4.5 cm.


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