# Ex.6.4 Q6 The-Triangle-and-its-Properties Solutions - NCERT Maths Class 7

## Question

The lengths of two sides of a triangle are \(\rm{}12\, cm\) and \(\rm{}15\,cm.\) Between what two measures should the lengths of third side fall.

## Text Solution

**What is known?**

The lengths of two sides of a triangle are \(12\) cm and \(15\) cm.

**What is unknown?**

Between what two measures should the lengths of third side fall.

**Reasoning:**

This question is straight forward. you just have to remember one property that the sum of lengths of any two sides of a triangle is always greater than the third side and also the difference between the length of any two sides of a triangle is smaller than the length of third side. In this question, two sides of a triangle are given as \(\rm{}12\,cm\) and \(\rm{}15\,cm\), find the sum and difference of this two sides. Remember, the third side should be lesser than their sum and also it should be greater than their difference.

**Steps:**

We know that, Sum of lengths of any two sides of a triangle is always greater than the

third side and also the difference between the lengths of any two sides is always smaller than the third side.

Hence the third side will be lesser than the sum of these two sides \(\rm{}12\,cm + 15\,cm =27\, cm\) and also it will be greater than the difference of these two sides \(\rm{}15\,cm – 12\,cm =3\,cm.\) Therefore, length of third side will be smaller than \(\rm{}27\,cm\) and greater than \(\rm{}3\,cm.\)