Construct a scalene triangle ABC, given AB $ = 3cm$ , AC $ = 5cm$ and BC $ = 4cm$ .

Hint: A triangle with all sides of different lengths is called a scalene triangle. To construct a triangle with the length of three sides given, we will use a ruler and a compass. We will first draw a line segment of the given length using a ruler. Then we will fix the length of the second segment in the compass using the ruler. We will place the tip of the compass on one end point of the drawn segment and mark an arc using the compass for the second segment. Similarly, we will draw the third segment to construct the triangle.

Complete step-by-step solution:
Let us draw the first segment , which is AC $ = 5cm$

Following figure,
Now, we will fix the distance between the compass to be $3cm$ , which is the length of the second segment. We will place the tip of the compass on the point A and mark an arc using the compass at a distance of $3cm$ . Then we will reset the distance in the compass to be equal to the length of the third segment, which is $4cm$ . Now, we will place the tip of the compass at the point C and mark an arc at a distance of $4cm$ . The two arcs that we have drawn should intersect at a point. This point of intersection is the vertex B of the triangle . It should look like the following figure.

Next , we will join the points C and B to form segment BC. It will look like the following figure

Then we will join the points A and B to form the third segment AB. We will get the required triangle of the specified side lengths and it will look like the following figure


Note: The construction in geometry should be very clear. It is beneficial to use a sharp pencil and a clean ruler and other instruments for construction. If there is a difference of even a millimeter in the given and actual measurements. Then the construction will not be accurate and we might end up with a wrong figure. Hence, all geometric constructions required precision.