Question
Download Solution PDFTaking any three of the line segments out of segments of length 2 cm, 5 cm, 7 cm and 8 cm, the number of triangles that can be formed is:
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFGiven:
Line segments: 2 cm, 5 cm, 7 cm, 8 cm
Formula used:
For any three line segments to form a triangle, the sum of any two sides must be greater than the third side.
Calculation:
Possible combinations:
1. 2 cm, 5 cm, 7 cm
⇒ 2 + 5 > 7 (False)
2. 2 cm, 5 cm, 8 cm
⇒ 2 + 5 > 8 (False)
3. 2 cm, 7 cm, 8 cm
⇒ 2 + 7 > 8 (True)
⇒ 2 + 8 > 7 (True)
⇒ 7 + 8 > 2 (True)
4. 5 cm, 7 cm, 8 cm
⇒ 5 + 7 > 8 (True)
⇒ 5 + 8 > 7 (True)
⇒ 7 + 8 > 5 (True)
Valid triangles: 2 cm, 7 cm, 8 cm and 5 cm, 7 cm, 8 cm
∴ The number of triangles that can be formed is 2. The correct answer is option 4.
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