- A5, 8, 11
- B2, 4, 8
- C3, 3, 9
- D1, 2, 3
Step-by-Step Solution
5+8=13>11 and the others hold, so 5,8,11 works. For 2,4,8: 2+4=6<8 (fails). For 3,3,9: 3+3=6<9 (fails). For 1,2,3: 1+2=3, not greater than 3 (fails).
Answer: A) 5, 8, 11
Which set of lengths can form a triangle?
Class 7The Triangle and its PropertiesTriangles
Key idea: Triangle inequality
**The sum of any two sides of a triangle is greater than the third side.**
So a triangle with sides 3, 4, 5 works (3+4>5, 3+5>4, 4+5>3). But sides 1, 2, 5 do NOT form a triangle — 1 + 2 = 3 is less than 5, so the two short sides can't reach across.
Use this to test whether three given lengths can be a triangle, or to bound a missing side: if two sides are 5 and 8, the third must be greater than 8 − 5 = 3 AND less than 8 + 5 = 13.
So a triangle with sides 3, 4, 5 works (3+4>5, 3+5>4, 4+5>3). But sides 1, 2, 5 do NOT form a triangle — 1 + 2 = 3 is less than 5, so the two short sides can't reach across.
Use this to test whether three given lengths can be a triangle, or to bound a missing side: if two sides are 5 and 8, the third must be greater than 8 − 5 = 3 AND less than 8 + 5 = 13.
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