A rectangle with dimensions \( 5 \) cm by \( 12 \) cm is inscribed in a circle. What is the number of centimeters in the circumference of the circle? Express your answer in terms of \( \pi \).

["Rectangle Inscribed in a Circle: Finding the Circumference Using Dimensions (5) cm by (12) cm", "When a rectangle is inscribed in a circle, the circle’s diameter equals the rectangle’s diagonal. Understanding this key geometry relationship allows us to compute the circle’s circumference precisely—even when only the rectangle’s sides are known.", "In this case, the inscribed rectangle measures (5) cm by (12) cm. To find the circle’s circumference, we first calculate the diagonal, which serves as the circle’s diameter.", "Using the Pythagorean Theorem:", "[\n\ ext{Diagonal} = \sqrt{(5)^2 + (12)^2} = \sqrt{25 + 144} = \sqrt{169} = 13 \ ext{ cm}\n]", "This diagonal (13 cm) is the diameter of the circumscribed circle. The circumference (C) of a circle is given by:", "[\nC = \pi \ imes \ ext{diameter}\n]", "Substituting the diameter:", "[\nC = \pi \ imes 13 = 13\pi \ ext{ cm}\n]", "Therefore, the circumference of the circle is (13\pi) centimeters. This elegant solution demonstrates how basic geometry—specifically the diagonal of an inscribed rectangle—provides a clear path to solving real-world measurement problems efficiently.", "Key Takeaway: When a rectangle with sides (5) cm and (12) cm is inscribed in a circle, the circle’s circumference is (13\pi) cm—directly derived from the Pythagorean diagonal as the diameter."]