- A8 cm
- B10 cm
- C16 cm
- D18 cm
Step-by-Step Solution
Third side must satisfy 7 < < 17 (since |12 − 5| = 7 and 12 + 5 = 17). 18 lies outside this range, so it cannot be the third side.
Answer: D) 18 cm
Two sides of a triangle measure 12 cm and 5 cm. Which of the following cannot be the length of the third side?
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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