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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In an isosceles triangle, two sides are equal. Given two sides are 6 cm and 12 cm. The third side must be equal to one of these to maintain the isosceles property.

Case 1: If the two equal sides are 6 cm each, then the third side is 12 cm.
Check triangle inequality: 6 + 6 > 12? 12 > 12 is false, so this is not a valid triangle.

Case 2: If the two equal sides are 12 cm each, then the third side is 6 cm.
Check triangle inequality: 12 + 12 > 6? 24 > 6 true, 12 + 6 > 12? 18 > 12 true, 12 + 6 > 12? 18 > 12 true.

So, the triangle with sides 12 cm, 12 cm, and 6 cm is valid.

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