- A5 cm
- B4 cm
- C1 cm
- D14 cm
Step-by-Step Solution
Third side > |9 − 5| = 4 and < 9 + 5 = 14, so the range is (4, 14). The smallest integer greater than 4 is 5.
Answer: A) 5 cm
What is the smallest possible integer value for the third side of a triangle with sides 5 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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