Question

Which of the following tools would you use to construct
$△ABC,\text{where}AB=5\text{cm},BC=5.4\text{cm, and}AC=4.9\text{cm}?$

• A. Divider and protractor
• B. Scale and protractor
• C. Scale and compass
• D. Compass and protractor

Answer 1

The correct option is C Scale and compass

Let’s first draw the line segment $AB=5\text{cm}.$


The length of the line segment $AC$ is $4.9\text{cm}$ .
This means that $C$ is $4.9\text{cm}$ away from point $A$.
But here the angles of the triangle are not known.
So we draw a circle of radius $4.9\text{cm}$ using a compass with $A$ as the center.



This circle will contain all the points that are $4.9\text{cm}$ away from $A$.
Similarly, $BC$ is $5.4\text{cm}$ which means that $C$ is at a distance of $5.4\text{cm}$ from $B$.
Let’s draw another circle of radius $5.4\text{cm}$ with center at $B$ using a compass.


Wherever the circles intersect will give us the location of point $C$.

In this entire construction, we’ve only used a scale and compass.