Mary wants to build a fence in the yard to keep her dog from running away. She only has 60 feet of fencing. If she wants to create a rectangular space that has a length that is twice as long as the width. How long is each side of the rectangular space?
Let's assume the width of the rectangular space is x feet.
According to the given information, the length is twice as long as the width, so the length would be 2x feet.
To calculate the perimeter of the rectangle, you add up all the sides:
Perimeter = 2(length) + 2(width)
Given that the perimeter is 60 feet, we can now set up the equation:
60 = 2(2x) + 2(x)
Simplifying the equation:
60 = 4x + 2x
Combine like terms:
60 = 6x
Divide both sides by 6:
x = 60/6
x = 10
Therefore, the width of the rectangular space is 10 feet. Since the length is twice as long, the length would be 2 times the width:
Length = 2(10) = 20
So, each side of the rectangular space would be 10 feet (width) and 20 feet (length).
To find out how long each side of the rectangular space is, we need to set up an equation based on the given information.
Let's denote the width of the rectangular space as "x" (in feet). According to the problem, the length is twice as long as the width, so the length would be "2x" (in feet).
Now, we know that the perimeter of a rectangle is found by adding up all of its side lengths. The perimeter of a rectangle can also be represented as the sum of twice the width and twice the length:
Perimeter = 2(Width) + 2(Length).
Plugging in the given values, we have:
60 = 2(x) + 2(2x).
Simplifying the equation, we get:
60 = 2x + 4x.
Combining like terms, we have:
60 = 6x.
Now, we can solve for x by dividing both sides of the equation by 6:
x = 60/6.
Simplifying the right side of the equation, we get:
x = 10.
Therefore, the width of the rectangular space is 10 feet. Since the length is twice the width, it would be 2 * 10 = 20 feet.
So, each side of the rectangular space is 10 feet for the width and 20 feet for the length.
Let x = width
Let 2x = length
Perimeter of rectangle:
P = 2*(length + width)
Substitute:
60 = 2*(2x + x)
60 = 2*3x
60 = 6x
x = 10 ft (width)
2x = 20 ft (length)