Is it possible to construct a triangle with lengths of its sides as 9 cm, 7 cm and 17 cm? Give reason for your answer.

Explanation

To determine if a triangle can be constructed with side lengths of 9 cm, 7 cm, and 17 cm, we will use the Triangle Inequality Theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

### Step-by-Step Solution:

1. **Identify the sides**: We have three sides of lengths 9 cm, 7 cm, and 17 cm.

2. **Apply the Triangle Inequality Theorem**: We need to check the following three conditions:
- Condition 1: \( a + b > c \)
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