Final answer:
To solve for the dimensions of a college athletic field with a perimeter of 92 meters and a length that is 12 meters more than the width, a system of equations is used to find that the width is 17 meters and the length is 29 meters.
Step-by-step explanation:
Finding the Length and Width of a College Athletic Field
To find the length and width of a college athletic field where the perimeter is 92 meters and the length is 12 meters more than the width, we can set up a system of equations. Let W represent the width and L represent the length. The perimeter P of a rectangle is calculated by the formula P = 2L + 2W. Given that the length L is 12 meters more than the width W, we can write L = W + 12.
Substituting the length in terms of the width into the perimeter formula gives us: 92 = 2(W + 12) + 2W. Simplifying this equation, we get 92 = 4W + 24. Subtracting 24 from both sides gives us 68 = 4W, and dividing both sides by 4 gives us W = 17 meters for the width. Now, to find the length, we substitute the width back into the equation for the length: L = W + 12, resulting in L = 17 + 12 = 29 meters.
Therefore, the width of the college athletic field is 17 meters, and the length is 29 meters.