A circular table is placed in a corner of a room so that it touches both walls. A mark is made on the edge of the table, exactly 18 inches from one wall and 25 inches from the other. What is the radius of the table?
To find the radius of the table, we can use the Pythagorean theorem.
Let's consider that the table is placed in the corner with one wall being the base of the right triangle, the other wall being the height, and the distance between the two marks being the hypotenuse.
Using the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides.
Let's call the distance from one wall to the mark as x, and the distance from the other wall to the mark as y.
Therefore, we have:
x² + y² = hypotenuse²
Substituting the given values from the problem:
x = 18 inches
y = 25 inches
(18)² + (25)² = hypotenuse²
324 + 625 = hypotenuse²
949 = hypotenuse²
To find the length of the hypotenuse (the distance between the two marks), we take the square root of both sides:
√949 = √hypotenuse²
Approximately, hypotenuse = 30.81 inches
Now, the radius of the table is half the length of the hypotenuse because the distance from the center to the edge of a circle is equal to the radius.
Therefore, the radius of the table is approximately 15.40 inches.