Question

Construct an equilateral triangle of height $3.2cm$

Answer 1

First observe that the altitudes from any vertex to the opposite sides of an equilateral triangle are all of equal length. Hence we can define the height of an equilateral triangle as this common value of three altitudes.
Steps of construction
$1$. Draw any line segment $XY$.
$2$. Take any point $M$ on $XY$. Draw $ZM\perp XY$.
$3$. With M as center and radius $3.2cm$, draw an arc, cutting $MZ$ at $A$.
$4$. Construct $\angle MAB={30}^{\circ }$ and $\angle MAC={30}^{\circ }$, with $B$ and $C$ on $XY$.
Then $ABC$ is the required triangle.