- A7
- B6
- C14
- D8
Step-by-Step Solution
Third side satisfies |9 − 4| < < 9 + 4, i.e. 5 < < 13. Integers 6, 7, 8, 9, 10, 11, 12 → 7 values.
Answer: A) 7
How many integer values can the third side of a triangle take if the other two sides are 4 cm and 9 cm?
Class 9Triangles (Congruence)Geometry — Triangles
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.
**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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