The length of a rectangular field is seven meters less than four times the width. The perimeter is 108 meter. Find the width and length of the field. How do I do this?
2l+2w=108
=2(4w-7)+2w=108
=8w-14+2w=108
=10w-14=108
=10w=122
=w=12.2m
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2l+2w=108
=2l+2(12.2)=108
=2l+24.4=108
=2l=83.6
=l=41.8m
To solve this problem, you can use the given information and solve it using algebraic equations. Let's assign variables to the dimensions of the rectangular field.
Let's assume:
- Width of the field = x meters
- Length of the field = 4x - 7 meters
To find the width and length of the field, we need to set up an equation using the given information about the perimeter.
Perimeter of a rectangle = 2 * (length + width)
Given that the perimeter is 108 meters, we can write the equation as:
2 * (4x - 7 + x) = 108
Let's simplify and solve the equation step by step:
2 * (5x - 7) = 108
10x - 14 = 108
10x = 108 + 14
10x = 122
x = 122 / 10
x = 12.2
Now that we have found the value of x, which represents the width of the field, we can substitute it back into the equation to find the length:
Length = 4x - 7
Length = 4 * 12.2 - 7
Length = 48.8 - 7
Length = 41.8
Therefore, the width of the field is approximately 12.2 meters, and the length is approximately 41.8 meters.