Question

Can we draw a triangle ABC with AB=3cm, BC=3.5cm and CA=6.5cm. Why?

Answer 1

Hint:
Apply the property of length of the sides of the triangle, which states that the sum of any two sides of the triangle should be greater than the third side. If there exists any pair of sides whose sum is equal to or less than the third side, then such a triangle is not possible.

Complete step by step solution:
We have to tell whether the given length of sides represents a triangle.
Now, we know that the sum of any two sides of the triangle should be greater than the third side. If there exists any pair of sides whose sum is equal to or less than the third side, then such a triangle is not possible.
Hence, we will make all possible combinations and check for the given condition.

Let us add AB and AC,
\[{\text{AB + AC = 3 + 6}}{\text{.5 = 9}}{\text{.5 > 6 = BC}}\]
Here, the sum of two sides is greater than third side.
Now, let us take the sum of BC and AC
\[{\text{BC + AC = 3}}{\text{.5 + 6}}{\text{.5 = 10 > 3 = AB}}\]
which is true condition for sides of triangle.
Similarly, take the sum of AB and BC
\[{\text{AB + BC = 3 + 3}}{\text{.5 = 6}}{\text{.5 = AC}}\]
But the length of the third side should be greater than the sum of the other two sides and here the sum of two sides is equal to the third side, which makes the condition of triangle false.

Hence, there does not exist any triangle ABC with AB=3cm, BC=3.5cm and CA=6.5cm.

Note:
Many students generally think that the sum of two sides should not be less than the third side, but one also has to write that the sum of two sides cannot be equal to the third side. The triangle is only possible when the sum of two sides is strictly greater than the third side. Even, if there is a single pair not satisfying the condition, the triangle will not be possible.