If the lengths of two sides of an isosceles triangle are 6 cm and 12 cm, then find the length of the third side.
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Correct answer: C
Explanation
The correct answer is option 3 i.e. 12 cm.
Let the two equal sides be 6 cm each.
In this case, the sides would be 6 cm, 6 cm, and 12 cm. But this violates the triangle inequality theorem, which states that the sum of any two sides of a triangle must be greater than the third side.
Let the two equal sides be 12 cm each.
In this case, the sides would be 12 cm, 12 cm, and 6 cm.
Here, 12 + 12 > 6, 12 + 6 > 12 and 6 + 12 > 12
All conditions of the triangle inequality theorem are satisfied.
Therefore, the length of the third side is 12 cm.