Question

Construct an equilateral triangle whose altitude is $5.4$ cm in length. The length of each side of the triangle is $k$. The nearest integer to $k$ is:

Answer 1

We know that in an equilateral triangle, all angles are equal to $={60}^0$ and the altitude bisects the opposite angle.
Hence, follow the steps given below to construct the triangle.
1. Draw a line $PQ$ and mark a point $D$ on it.
2. Construct a perpendicular of length $DA=5.4cm$ to $PQ$ at point $D$
3. Construct $\angle DAR=\frac{{60}^0}{2}={30}^0$ to intersect $PQ$ at $B$
4. Measure $BD$ and cut off an arc on $PQ$ of same distance $DC$ on the other side of $D$
5. Join $A$ to $C$
6. $ABC$ is the required equilateral triangle.

Measuring the length of the sides gives $AB=AC=BC=6.2cm$

$\therefore k=6$