Question

Construct an equilateral triangle whose altitude is 4cm.​

Answer 1

Answer

Step-by-step explanation:

1. Draw a line XY.

2. Mark any point D on XY.

3. From D, draw DE perpendicular to XY.

4. From D, set off DA=4cm, cutting DE at A.

5. Construct angle DAC=30°, meeting XY at B and C respectively.

Then, ∆ABC is required equilateral triangle.

Verification:-

on measuring, we find that

angle A= angle B= angle C= 60°

and AB = BC = CA = 4.5 cm

Justification:-

In ∆DAB, we have

angle ABD+ angle BDA+ angle DAB =180°

=} angle ABD+ 90°+30°=180°

=} angle ABD=180°-120°= 60°

In ∆ABC, we have

angle A= angle B= angle C=60°

Hence, ∆ABC is an equilateral triangle.