# Ex.6.4 Q1 The-Triangle-and-its-Properties Solutions - NCERT Maths Class 7

## Question

Is it possible to have a triangle with the following sides?

(i) \(\rm{}2\, cm,\) \(\rm{}3\,cm,\) \(\rm{}5\, cm\)

(ii) \(\rm{}3 \,cm, 6\, cm, 7\, cm \)

(iii) \(\rm{}6 \,cm, 3\, cm, 2\,cm\)

## Text Solution

**What is known? **

Sides of triangle.

**What is unknown? **

Is it possible to have a triangle with these sides.

**Reasoning:**

This problem is based on a very simple property that if the sum of lengths of any two sides of a triangle is greater than the third side, then it is possible to draw a triangle. By using this property, you just have to check by taking the sum of any two sides of a triangle whether it is greater than the third side or not. For better understanding take any two sides one by one and check if sum of these two sides is greater than the third side or not, if it is greater than the third sides then it is possible to draw a triangle.

(i) \(\rm{}2+3>5\) No

\(\rm{}3+5>2\) Yes

\(\rm{}5+2>3\) Yes

No, the triangle is not possible

(ii) \(\rm{}3+6>7\) Yes

\(\rm{}6+7>3\) Yes

\(7+3>3\) Yes

Yes, the triangle is possible

(iii) \(\rm{}6+3>2\) Yes

\(\rm{} 3+2>6 \) No

\(\rm{}2+6>3\) Yes

No, the triangle is not possible

**Useful Tip**

Whenever you encounter problems of this kind, it is best to think of the property based on sum of lengths of any two sides of a triangle.

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