Construct the following and give justification :

An equilateral triangle if its altitude is 3.2 cm.

Answers (2)

Given : An equilateral triangle with Altitude : 3.2 cm

            Steps of Construction :

            1.         Draw a line XY and take a point D on it .

            2.         Draw line DE with 90^{\circ} angle at D.

            3.         Cut the line DE with arc of radius 3.2 cm at point A

            4.         Make an angle of 30^{\circ} at A which cuts XY at B.

            5.         Now find the length of BD and as center D cut the line XY at point C with radius equal to BD.

            6.         Join AC

            ABC is the required triangle.

           

            Justification :

            Here \angle A = \angle BAD + \angle CAD

                       =30^{\circ}+30^{\circ}=60^{\circ}

                     AD\perp XY

            In DABD,\angle BAD + \angle DBA + \angle ADB = 30^{\circ}+60^{\circ}+90^{\circ}=180^{\circ}

                    \angle A = \angle B = \angle C = 60^{\circ}

            Hence it is an equilateral triangle.

 

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