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An isosceles triangle has two equal sides of 5 cm each. Which of these CANNOT be the length of its base?

Class 7The Triangle and its PropertiesTriangles
  • A9 cm
  • B10 cm
  • C3 cm
  • D1 cm

Step-by-Step Solution

The base must be less than 5 + 5 = 10 cm. At exactly 10 cm the two equal sides would lie flat along the base, forming a straight line rather than a triangle, so 10 cm is impossible; 9 cm, 3 cm and 1 cm all work. Trap: reading "sum of two sides > third" as "sum of two sides is at least the third" and allowing the boundary value.
Answer: B) 10 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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