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r = \frac{26}{2} = 13 \text{ cm}
The circumference $C$ of the circle is:
C = 2\pi r = 2\pi(13) = 26\pi
\boxed{26\pi}
Question: An aerospace engineer at Blue Origin is designing a triangular support beam with side lengths of 13 cm, 14 cm, and 15 cm. What is the length of the shortest altitude, in centimeters?
Solution: First, we compute the area of the triangle using Heron’s formula. The semi-perimeter $s$ is:
s = \frac{13 + 14 + 15}{2} = 21 \text{ cm}
The area $A$ is:
A = \sqrt{s(s - a)(s - b)(s - c)} = \sqrt{21(21 - 13)(21 - 14)(21 - 15)} = \sqrt{21 \cdot 8 \cdot 7 \cdot 6}
A = \sqrt{7056} = 84 \text{ cm}^2