the perimeter of an athletic field is 104 meters and the length is 12 meters more than the width find the width and the length.
Width = W meters.
Length = (W+12) meters.
2W + 2(W+12) = 104 meters.
2W + 2W + 24 = 104.
4W = 104 - 24 = 80
W = 20 meters.
W+12 = 20 + 12 = 32 meters.
To find the dimensions of the athletic field (width and length), we can set up a system of equations based on the given information.
Let's assume the width of the field is represented by the variable "w" (in meters).
According to the given information, the length of the field is 12 meters more than the width. So, the length can be represented by the expression "(w + 12)".
The perimeter of a rectangle is calculated by adding up all its sides. For a rectangular field, the perimeter is the sum of the lengths of all four sides.
Since opposite sides of a rectangle are equal, the perimeter can be calculated as:
Perimeter = 2 * (Length + Width)
Given that the perimeter is 104 meters, we can now set up the equation:
104 = 2 * ((w + 12) + w)
Now, let's solve this equation to find the value of "w" (width).
104 = 2 * (2w + 12)
Divide both sides by 2:
52 = 2w + 12
Subtract 12 from both sides:
40 = 2w
Divide both sides by 2:
20 = w
Therefore, the width of the athletic field is 20 meters.
To find the length, substitute the value of "w" back into the expression (w + 12):
Length = w + 12 = 20 + 12 = 32
Hence, the length of the athletic field is 32 meters.