Can a triangle have sides 6 cm, 6 cm, and 10 cm?

Class 7The Triangle and its PropertiesTriangles

AYes, because 6 + 6 is greater than 10
BNo, because two of the sides are equal
CNo, because 10 is longer than 6
DIt cannot be told without measuring the angles

Step-by-Step Solution

Check: 6+6=12>10; 6+10=16>6; 6+10=16>6. All hold, so the triangle is valid (an isosceles triangle).

Answer: A) Yes, because 6 + 6 is greater than 10

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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