To determine the dimensions of a square sports arena given its area, we begin with understanding the formula for the area of a square. The area [tex]\( A \)[/tex] of a square is calculated using the formula:
[tex]\[ A = \text{side}^2 \][/tex]
Given:
[tex]\[ A = 10,000 \, \text{m}^2 \][/tex]
To find the side length of the square, we need to solve for the side. This requires taking the square root of the given area. The side length [tex]\( s \)[/tex] can be found using the formula:
[tex]\[ s = \sqrt{A} \][/tex]
Substituting the given area into the formula:
[tex]\[ s = \sqrt{10,000} \][/tex]
Calculating the square root of 10,000:
[tex]\[ s = 100 \, \text{meters} \][/tex]
Therefore, the length of each side of the square sports arena is 100 meters.
Since a square has all four sides of equal length, the dimensions of the sports arena are:
[tex]\[ \text{Length} = 100 \, \text{meters} \][/tex]
[tex]\[ \text{Width} = 100 \, \text{meters} \][/tex]
Thus, the dimensions of the sports arena are [tex]\( 100 \)[/tex] meters by [tex]\( 100 \)[/tex] meters.
