The perimeter of a rectangular field is 380 yd. The length is 10 yd longer than the width. Find the dimensions.
Please help and show work thank you
P = 2L + 2W
380 = 2(W + 10) + 2W
380 = 4W + 20
360 = 4W
90 = width
The perimeter of a rectangular field is 380 yd. The length is 90 yd longer than the width. Find the dimensions.
The perimeter of a rectangular field is yd. The length is yd longer than the width. Find the dimensions.
The larger of the two sides is
nothing yd.
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Now, let's solve the problem.
Let's say the width of the rectangular field is "x" yards.
According to the problem, the length is 10 yards longer than the width, so the length would be "x + 10" yards.
The formula for the perimeter of a rectangle is P = 2(length + width).
In this case, the perimeter is given as 380 yards, so we can set up the equation as:
380 = 2(x + (x + 10))
Simplifying the equation:
380 = 2(2x + 10)
380 = 4x + 20
360 = 4x
x = 90
So, the width of the field is 90 yards, and the length is x + 10, which is 90 + 10 = 100 yards.
Therefore, the dimensions of the field are 90 yards by 100 yards.
To solve this problem, we can set up a system of equations based on the given information. Let's let "x" represent the width of the rectangular field.
1. First, we can use the formula for the perimeter of a rectangle to set up an equation: P = 2L + 2W, where P is the perimeter, L is the length, and W is the width.
In this case, we know that the perimeter is 380 yd, so we can write the equation as: 380 = 2L + 2W.
2. The problem also states that the length is 10 yd longer than the width, so we can write another equation: L = W + 10.
Now we have a system of equations:
Equation 1: 380 = 2L + 2W,
Equation 2: L = W + 10.
To solve this system, we can use the substitution method.
3. Substitute the expression for L from Equation 2 into Equation 1:
380 = 2(W + 10) + 2W.
Distribute 2 to the terms inside the parentheses:
380 = 2W + 20 + 2W.
Combine like terms:
380 = 4W + 20.
4. Subtract 20 from both sides of the equation:
360 = 4W.
5. Divide both sides by 4 to isolate W:
W = 90.
6. Now that we know the width, we can substitute this value back into Equation 2 to find the length:
L = 90 + 10 = 100.
Therefore, the dimensions of the rectangular field are 90 yards (width) and 100 yards (length).