Answer:
100 meters by 100 meters
Explanation:
To find the dimensions of the sports arena on the map, we first need to determine the length of each side of the square arena.
Given that the area of the square arena is 10,000 square meters, we can use the formula for the area of a square:
\[Area = \text{Side}^2\]
Let's solve for the side length:
\[10,000 = \text{Side}^2\]
To find the side length, take the square root of both sides:
\[\sqrt{10,000} = \sqrt{\text{Side}^2}\]
\[100 = \text{Side}\]
So, each side of the square arena is 100 meters.
Now, let's consider the map. If the map is a scale representation of the area, we need to determine the scale. If no scale is provided, we'll assume that 1 unit on the map represents 1 meter in reality (a 1:1 scale).
Therefore, the dimensions of the sports arena on the map are also 100 meters by 100 meters, which means it's a square with sides measuring 100 units on the map.