A court is 94ft long by 50ft wide. It has 3 circles each 12ft diameter. Two of the circles are at the free throw line and the third is at the center of the court. Within the 3rd circle is another circle with a radius of 2ft.The key is rectangular region on the court from the free throw line.The backboard is 4 ft from the baseline. **Is the key similar to the basketball court?Explain?**Is the inner circle similar to the entire circle in the center of the court? Explain?
you give no dimensions of the key's rectangle. Its sides must be in the ratio of 94:50 to be similar to the court.
All circles are similar to each other.
To determine if the key is similar to the basketball court, we need to compare their corresponding attributes.
The key is described as a rectangular region on the court from the free-throw line. Given that the court is 94ft long by 50ft wide, we can calculate the dimensions of the key.
The key's length is from the free-throw line to the baseline, which is the same as the length of the court, 94ft. Its width is 16ft, which is the distance between the free-throw line and the top of the key.
On the other hand, the basketball court is rectangular with dimensions of 94ft long by 50ft wide. Comparing these dimensions, we can conclude that the key is a smaller rectangular region within the larger basketball court. Therefore, they are not similar.
Now let's consider the inner circle within the center circle of the court. The center circle has a diameter of 12ft, and inside it, there is another circle with a radius of 2ft.
To determine if the inner circle is similar to the entire circle in the center of the court, we need to compare their attributes.
Both circles have the same center, which is the center of the court. However, their radii are different; the inner circle has a radius of 2ft, while the center circle has a radius of 6ft (half of its diameter).
Since the radii of the two circles are different, we can conclude that they are not similar.
In conclusion, the key and the basketball court are not similar, and the inner circle is not similar to the entire circle in the center of the court.