Solved Examples Example 1: Can we form a triangle with line segments of lengths 7 cm, 8 cm and 13 cm?
Solution: The sum of the lengths of the two smaller line segments = 7 cm +8 cm = 15 cm.
The length of the longest line segment = 13 cm.
Thus, the sum of the lengths of two the smaller line segments is greater than the length
the longest line segment.
Hence, the line segments of lengths 7 cm, 8 cm and 13 cm can form a triangle,
Example 2: Is it possible to form a triangle whose sides are 5 cm, 6 cm and 12 cm long?
Solution: Let us consider three line segments of lengths 5 cm, 6 cm and 12 cm.
The sum of the lengths of the two smaller line segments = 5 cm + 6 cm = 11 cm.
The length of the longest line segment = 12 cm.
Thus, the sum of the lengths of two smaller line segments is not greater than the lengt
the longest line segment.
So, it is not possible to form a triangle by the three line segments of lengths 5 cm, 6 cm
12 cm.
Solution: The sum of the lengths of the two smaller line segments = 7 cm +8 cm = 15 cm.
The length of the longest line segment = 13 cm.
Thus, the sum of the lengths of two the smaller line segments is greater than the length
the longest line segment.
Hence, the line segments of lengths 7 cm, 8 cm and 13 cm can form a triangle,
Example 2: Is it possible to form a triangle whose sides are 5 cm, 6 cm and 12 cm long?
Solution: Let us consider three line segments of lengths 5 cm, 6 cm and 12 cm.
The sum of the lengths of the two smaller line segments = 5 cm + 6 cm = 11 cm.
The length of the longest line segment = 12 cm.
Thus, the sum of the lengths of two smaller line segments is not greater than the lengt
the longest line segment.
So, it is not possible to form a triangle by the three line segments of lengths 5 cm, 6 cm
12 cm.
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