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Two sides of a triangle are 12 cm and 5 cm. Which of these can be the length of the third side?

Class 7The Triangle and its PropertiesTriangles
  • A7 cm
  • B17 cm
  • C9 cm
  • D4 cm

Step-by-Step Solution

The third side must be greater than 12 − 5 = 7 and less than 12 + 5 = 17, so 7 < < 17. Only 9 cm lies strictly inside that range. Trap: accepting the boundary values 7 cm or 17 cm — at exactly those lengths the sides collapse into a straight line (5 + 7 = 12 and 12 + 5 = 17), so the inequality must be strict.
Answer: C) 9 cm

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.

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