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Can a triangle have sides 3 cm, 4 cm, and 8 cm?

Class 9Triangles (Congruence)Geometry — Triangles
  • ANo, because 3 + 4 is less than 8
  • BYes, because all the sides are positive
  • CYes, because 8 is the longest side
  • DNo, because the sides are all different

Step-by-Step Solution

3 + 4 = 7 < 8. The two smaller sides do not sum to more than the largest, so the triangle inequality fails.
Answer: A) No, because 3 + 4 is less than 8

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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