The length of a rectangular football field is 14 meters more than twice its width. If the perimeter is 346 meters, find the field's dimensions.
P = 2L + 2W
346 = 2(2W + 14) + 2W
346 = 6W + 28
318 = 6W
53 = W
Let's denote the width of the rectangular football field as "w" meters.
According to the given information, the length of the field is 14 meters more than twice its width, which can be expressed as "2w + 14" meters.
The formula for the perimeter of a rectangle is given by: P = 2l + 2w, where "P" denotes the perimeter, "l" denotes the length, and "w" denotes the width.
Given that the perimeter is 346 meters, we can set up the equation as follows:
346 = 2(2w + 14) + 2w
Let's solve this equation step-by-step:
1. Simplify the equation:
346 = 4w + 28 + 2w
2. Combine like terms:
346 = 6w + 28
3. Subtract 28 from both sides of the equation:
346 - 28 = 6w
4. Simplify:
318 = 6w
5. Divide both sides of the equation by 6:
w = 318/6
6. Perform the division:
w = 53
7. Hence, the width of the football field is 53 meters.
To find the length, we substitute the value of "w" back into the expression for the length:
Length = 2w + 14
Length = 2(53) + 14
Length = 106 + 14
Length = 120
Therefore, the dimensions of the football field are a width of 53 meters and a length of 120 meters.
To find the dimensions of the rectangular football field, we can set up two equations based on the given information.
Let's assume the width of the field is 'w' meters.
The length of the field is given as "14 meters more than twice its width," which can be written as:
Length = 2w + 14
The perimeter of a rectangle is given by the formula:
Perimeter = 2(Length + Width)
Plugging in the given perimeter value of 346 meters:
346 = 2(2w + 14 + w)
Simplifying the equation:
346 = 2(3w + 14)
346 = 6w + 28
6w = 346 - 28
6w = 318
w = 318/6
w = 53
Therefore, the width of the field is 53 meters.
Plugging this value back into the equation for the length:
Length = 2w + 14
Length = 2(53) + 14
Length = 106 + 14
Length = 120
Therefore, the length of the field is 120 meters.
Thus, the dimensions of the rectangular football field are:
Width = 53 meters
Length = 120 meters.