Find the radius of a circle circumscribed about a rectangle whose two sides are 11√135.
| July 27, 2021 | education
The diameter of a circle circumscribed about a rectangle is equal to its diagonal. Two adjacent sides of a rectangle and its diagonal form a right-angled triangle in which the diagonal is the hypotenuse. Find the square of the diagonal by the Pythagorean theorem:
d ^ 2 = 11 ^ 2 + (√135) ^ 2 = 121 + 135 = 256;
d = √256 = 16.
Knowing that the diameter of the circumscribed circle is 16, we find the radius:
r = d / 2 = 16/2 = 8.
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