Sides of a triangle are 6 cm, 8 cm and 13 cm. Can such a triangle exist?

Class 9Triangles (Congruence)Geometry — Triangles

AYes, because the sum of any two sides is greater than the third
BNo, because 6 + 8 is too close to 13
CNo, because 13 is more than double 6
DIt cannot be told without measuring the angles

Step-by-Step Solution

Check: 6 + 8 = 14 > 13 ✓; 6 + 13 > 8 ✓; 8 + 13 > 6 ✓. All conditions hold, so the triangle exists.

Answer: A) Yes, because the sum of any two sides is greater than the third

Key idea: Inequalities in a triangle

**Property 1**: In a triangle, the side opposite the LARGER angle is LONGER. (Bigger angle stretches the opposite side.)

**Property 2**: Conversely, the angle opposite the longer side is larger.

**Property 3 (Triangle Inequality)**: The sum of any two sides of a triangle is GREATER than the third side.

This means three given lengths form a triangle ONLY IF each pair sums to more than the third.

Example: Can 2, 3, 6 form a triangle? Check: 2 + 3 = 5 < 6. NO.

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