Construct an equilateral triangle of height 4.5 cm. Measure approximate length of the its side.

An equilateral triangle has three equal sides and each angle measuring 60°. To make an equilateral triangle, we have been given height of the triangle and we already know the sides are all equal.

Steps of construction:

1. Draw a line segment XY, large enough using a ruler.

2. Take any point M on line segment XY. Draw ZM ⊥ XY using a compass and ruler.

To draw perpendicular ZM: With M as centre, draw a circle/semicircle of radius say 4 cm cutting the line XY at P and Q on XY. Taking each P and Q as centre, draw an arc or circle of radius 3 cm (say). These arcs or circle should intersect the circle of centre M. The points at which they intersect, draw two more arcs or circles of radius 4.2 cm. Let the point at which these arcs or circles intersect be Z. Join MZ.

3. With M as centre and radius 4.5 cm, draw an arc/circle/semicircle cutting MZ at A using a compass.

4. Construct ∠MAB = 30° and ∠MAC = 30°, with B and C on XY using a compass.

To measure the length of sides of the equilateral triangle, use a ruler and measure the length of one of the sides of the triangle so constructed.

Here, the length has come out to be 5.2 cm.

Thus, ABC is the required equilateral triangle and the length of its sides is 5.2 cm.