- A4
- B5
- C18
- D9
Step-by-Step Solution
Third side must satisfy 10 − 7 < < 10 + 7, i.e. 3 < < 17. So 4, 5, and 9 all work. 18 is not less than 17, so 18 cannot be the third side.
Answer: C) 18
Two sides of a triangle are 7 and 10. Which value cannot be the third side?
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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