Question

The lengths of two sides of a triangle are 12cm and 15cm. between what two measures should the length of the third side fall?

Answer 1

Hint: - Here we have to go through the properties of the construction of triangles as we know that the sum of two sides is greater than the third side.

Complete step-by-step answer:
Here in the question it is given that the lengths of two sides of a triangle are 12cm and 15cm.
Since, the sum of lengths of any two sides in a triangle should be greater than the length of the third side for the formation of a triangle.
Therefore, the third side should be less than 12+15=27cm.
And also we know that the third side cannot be less than the difference of the two sides.
Therefore, the third side has to be more than 15−12=3cm.
By the above results we can say that the third side should be the length more than 3cm and less than 27cm.
$\therefore 3cm < {3^{rd}}side < 27cm$

Note: - Whenever we face such a type of question the key concept for solving the question is to first write down the given sides of the triangle and then apply the properties of the triangle to find out the ranges of the side of the triangle. You should always remember the concept of triangles to solve such a type of question.