The perimeter of a rectangular piece of property is 8 miles and it's area is 3 square miles, find the dimensions
Let's assume the length of the rectangular property is L miles and the width is W miles.
The perimeter of the rectangular property is given by the formula:
Perimeter = 2(L + W)
Since the perimeter is given as 8 miles, we can write the equation:
2(L + W) = 8
Simplifying this equation, we have:
L + W = 4
The area of the rectangular property is given by the formula:
Area = L * W
Since the area is given as 3 square miles, we can write the equation:
L * W = 3
Now, we have two equations:
Equation 1: L + W = 4
Equation 2: L * W = 3
We can solve these equations simultaneously to find the dimensions of the rectangular property.
From Equation 1, we can write:
L = 4 - W
Substituting this value of L in Equation 2, we have:
(4 - W) * W = 3
Expanding the equation, we get:
4W - W^2 = 3
Rearranging the equation, we have:
W^2 - 4W + 3 = 0
Factoring the quadratic equation, we have:
(W - 3)(W - 1) = 0
This gives us two possible values for W:
W = 3 or W = 1
If W = 3, then L = 4 - 3 = 1
If W = 1, then L = 4 - 1 = 3
Therefore, the dimensions of the rectangular property can be either 1 mile by 3 miles or 3 miles by 1 mile.
To find the dimensions of the rectangular property, we can start by setting up two equations based on the given information.
Let's assume the length of the property is L miles and the width is W miles.
1. Perimeter equation:
The perimeter of a rectangle is given by the formula P = 2L + 2W. In this case, the perimeter is given as 8 miles, so we can write the equation as:
2L + 2W = 8
2. Area equation:
The area of a rectangle is given by the formula A = L * W. In this case, the area is given as 3 square miles, so we can write the equation as:
L * W = 3
Now, we have two equations with two variables. We can solve them simultaneously to find the dimensions.
To eliminate one variable, we can rewrite the perimeter equation as:
L + W = 4 (by dividing the entire equation by 2)
Next, we can solve the elimination method by substituting (4 - W) in place of L in the area equation:
(4 - W) * W = 3
4W - W^2 = 3
Rearranging this equation:
W^2 - 4W + 3 = 0
Now, we can factor this quadratic equation:
(W - 1)(W - 3) = 0
This gives us two possible values for W: W = 1 and W = 3.
For W = 1, substituting this value back into the perimeter equation, we get:
L + 1 = 4
L = 3
For W = 3, substituting this value back into the perimeter equation, we get:
L + 3 = 4
L = 1
Therefore, there are two possible dimensions for the rectangular property:
1) Length = 3 miles and Width = 1 mile
2) Length = 1 mile and Width = 3 miles