a circular table is pushed in the corner of a rectangular room such that it touches the two perpendicular walls of the room. A point on the periphery of the table such that it is 9 units from one wall and 8 units from the other wall. find the radius of the table
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To find the radius of the table, we can use the Pythagorean theorem.
Let's assume that the distances from the point on the periphery of the table to the walls are represented by the legs of a right triangle, with one leg measuring 9 units and the other leg measuring 8 units. The hypotenuse of this right triangle will be the radius of the circular table.
Using the Pythagorean theorem, which states that the square of the hypotenuse is equal to the sum of the squares of the other two sides, we can calculate the radius:
radius^2 = 9^2 + 8^2
radius^2 = 81 + 64
radius^2 = 145
To find the radius, we take the square root of both sides:
radius = sqrt(145)
Thus, the radius of the circular table is approximately 12.04 units.
To find the radius of the circular table, we can use the Pythagorean theorem.
Let's assume that the rectangular room has sides of length 'a' and 'b', with 'a' being the distance between the two perpendicular walls and 'b' being the perpendicular distance from the corner to the point on the periphery of the table.
According to the given information, we have:
One side of the rectangular room = a
The other side of the rectangular room = b
Distance from the point on the periphery of the table to one wall = 9 units
Distance from the point on the periphery of the table to the other wall = 8 units
We can now form the following right-angled triangle:
- One side of the triangle is the distance from the point on the periphery of the table to one wall, which is 9 units.
- Another side of the triangle is the distance from the point on the periphery of the table to the other wall, which is 8 units.
- The hypotenuse of the triangle is the diameter of the circular table, which is twice the radius.
Applying the Pythagorean theorem, we get:
(radius)^2 = (distance to one wall)^2 + (distance to other wall)^2
(radius)^2 = (9 units)^2 + (8 units)^2
(radius)^2 = 81 + 64
(radius)^2 = 145
Therefore, the radius of the circular table is the square root of 145 units.
(radius) = √145
(radius) ≈ 12.04 units
Hence, the radius of the circular table is approximately 12.04 units.