Final answer:
The converse of the Pythagorean theorem is true for lengths 11cm, 60cm, and 61cm as they satisfy the relationship a² + b² = c², which verifies that the triangle is a right triangle.
Step-by-step explanation:
The converse of the Pythagorean theorem is a mathematical proposition that states if the sum of the squares of two sides of a triangle equals the square of the longest side, then the triangle is a right triangle. Given the lengths 11cm, 60cm, and 61cm, the converse of the Pythagorean theorem can be tested. We need to verify whether the square of 60cm plus the square of 11cm equals the square of 61cm:
a² + b² = c²
60² + 11² = 61²
3600 + 121 = 3721
3721 = 3721
Since 3600 (60²) plus 121 (11²) equals 3721 (61²), the converse of the Pythagorean theorem holds true for these lengths, and the triangle is a right triangle. Therefore, the correct answer to the question is A. True.