The length of a rectangular playing field is 5ft. less than twice its width. If the perimeter of the playing field is 230ft, find the lenght and width of the field.
2W+2L= perimeter = 230
L=2W-5
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Solve these simultaneous equations.
Post your work if you need further assistance.
a small farm field is a square measuring 340 ft on a side. what is the perimeter of the field?
To solve this problem, we can use the given information and the equations provided.
Let W represent the width of the playing field, and L represent the length of the playing field.
The perimeter of a rectangle is given by the formula P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
From the problem, we are given that the perimeter of the playing field is 230ft. So, we can write the equation as:
2L + 2W = 230 ----(1)
We are also given that the length of the playing field is 5ft less than twice its width. So, we can write the equation as:
L = 2W - 5 ----(2)
Now, we have a system of two equations with two variables. We can solve this system by substitution or elimination method.
Let's solve it using the substitution method:
Step 1: Substitute the value of L from equation (2) into equation (1):
2(2W - 5) + 2W = 230
Step 2: Simplify the equation:
4W - 10 + 2W = 230
6W - 10 = 230
Step 3: Add 10 to both sides of the equation:
6W = 240
Step 4: Divide both sides of the equation by 6:
W = 40
Now that we have the value of W, we can substitute this value back into equation (2) to find L:
L = 2(40) - 5
L = 80 - 5
L = 75
Therefore, the length of the field is 75ft and the width is 40ft.