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

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 "> XY.

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 $6 \mathrm{~cm}$.

 

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