Question

Is it possible to have a triangle with sides having a measure of 6 cm, 3 cm, 2 cm?

Answer 1

Hint- Here, we will proceed by using one of the properties of the triangle which is that the sum of the lengths of any two sides of the triangle should always be greater than the length of the third side.

Complete step-by-step answer:

According to the property of the triangle, the sum of the lengths of any two sides of the triangle should always be greater than the length of the third side.
For any triangle ABC, all of the below mentioned inequalities must satisfy:
AB+BC>AC
AB+AC>BC
BC+AC>AB
Now, we have to find whether a triangle can be constructed with the length of the sides as 6 cm, 3 cm and 2 cm.
Here, let us suppose AB=6 cm, BC=3 cm and AC=2 cm. Now, we will check whether all of the above mentioned three inequalities are getting satisfied or not.
AB+BC = 6+3 = 9 cm and AC=2 cm
Clearly, AB+BC>AC
So, the first inequality is satisfied.
Also, AB+AC = 6+2 = 8 cm and BC=3 cm
Clearly, AB+AC>BC
So, the second inequality is satisfied.
Also, BC+AC = 3+2 = 5 cm and AB=6 cm
Clearly, BC+AC So, the third inequality is not satisfied.
Therefore, the third required inequality is not getting satisfied, so it is not possible to have a triangle with sides having a measure of 6 cm, 3 cm, 2 cm.

Note- In this particular problem, the given sides do not constitute any triangle. But if the sides given are such that the sum of the lengths of any two sides is greater than the length of the third side of the triangle, then these given sides forms a triangle and this triangle can be further classified as scalene or isosceles or equilateral triangle according to the measure of the sides given.