We want to determine whether we can construct one, many, or noscalene triangles with side lengths of 3 centimeters and 7 centimeters. We can recall that a scalene triangle is a triangle in which all three sides have different lengths.
We know that the missing side can be neither 3 centimeters nor 7 centimeters long. Now we can use a ruler and compass to draw our triangle. First we will draw a 7-centimeter side.
To find the position of the third vertex, we can open the compass to 3 centimeters. Then we can put the compass at one of the vertices and draw an arc.
We can recall that a triangle can be formed when the sum of the lengths of any two sides is greater than the length of the third side. Let's compare the side lengths using a table! We can denote the third side length with an arbitrary variable x.
Comparison
3cm+7cm? >x cm
3cm+xcm? >7cm
xcm+7cm? >3cm
10cm > xcm
xcm > 4cm
xcm > - 4cm
Notice that the missing side length has to be between 4 centimeters and 10 centimeters. This means that we can construct many triangles with the given description.
