Question:
Construct an equilateral triangle each of whose altitudes measures 5.4 cm. Measure each of its sides.
Solution:
Steps of construction:
1. Draw a line XY.
2. Mark any point P.
3. From P draw PQ
4. From $P$, set off $P A=5.4 \mathrm{~cm}$, cutting $P Q$ at $A$.
5. Construct $\angle P A B=30^{\circ}$ and $\angle P A C=30^{\circ}$, meeting $X Y$ at $B$ and $C$, respectively.
Thus, $\triangle A B C$ is the required triangle. Measure of each side is $6 \mathrm{~cm}$.