Question

Construct an equilateral triangle each of whose altitudes measures 5.4 cm.

Answer 1

Steps of construction:
1. Draw a line XY.
2. Mark any point P.
3. From P draw PQ $\perp$ XY.
4. From P, set off PA = 5.4 cm, cutting PQ at A.
5. Construct $\angle$PAB = 30$°$ and $\angle$PAC = 30$°$, meeting XY at B and C, respectively.

Thus, $△$ABC is the required triangle.