单选题What is the circumference of a circle in which a 5 by 12 rectangle is inscribed?A13nB17nC26nD34nE60n
单选题
What is the circumference of a circle in which a 5 by 12 rectangle is inscribed?
A
13n
B
17n
C
26n
D
34n
E
60n
参考解析
解析：
The length of a diagonal of a 5 by 12 rectangle is 13 since, when a diagonal is drawn, the lengths of the sides of the right triangle that results form a (5,12,13) Pythagorean triple with 13 as the hypotenuse. If this rectangle is inscribed in a circle, the diagonals of the rectangle are diameters of the circle, so the length of a diameter of the circle is 13. The circumference of a circle with diameter 13 is 13π.
The length of a diagonal of a 5 by 12 rectangle is 13 since, when a diagonal is drawn, the lengths of the sides of the right triangle that results form a (5,12,13) Pythagorean triple with 13 as the hypotenuse. If this rectangle is inscribed in a circle, the diagonals of the rectangle are diameters of the circle, so the length of a diameter of the circle is 13. The circumference of a circle with diameter 13 is 13π.
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