In a gymnasium, athletes perform their exercises on a square-based tumbling mat with an area of 1681 square feet. Determine the distance an athlete has to run along one side of the mat.
In this question about athletes exercising on a mat, what we really need to focus on is that this is a square mat with a given area. And we need to work out simply the distance of one side of this square. Since the mat is a square, we know that all sides will be the same length. So we can have a length and a width both of side length 𝑠.
To find the area of a square, we multiply the side by the side. We can write that as 𝑠 times 𝑠 equals 𝐴 for area. When we have a value such as 𝑠 multiplied by itself, we can write this as 𝑠 squared. We’re told that the area of this square mat is 1681. So we can plug that into our equation. To find our value 𝑠, we’re going to need to take the square root. And since we’re taking the square root of 𝑠 squared, we also need to take the square root of the value on the other side of the equation. The value of the square root of 𝑠 squared here will simply be 𝑠.
To find the value of 𝑠, we simply need to plug the square root of 1681 into our calculator. And that will give us an answer of 41. To find the units in this answer, we can see that our area was given in the area units square feet. And that means that our side length units will be 41 feet.
And so we know that the distance the athlete would have to run along one side of the mat is 41 feet.