) Brian has 96 feet of fencing to enclose a rectangular space in his
yard for his dog. He wants the rectangle to be twice as long as it
is wide.
Write and solve an equation to find the dimensions of the rectangle.
Let x = one side and 2x = the longer side
2x + 2(2x) = 96
Solve for x.
16
To find the dimensions of the rectangle, we need to set up an equation based on the given information.
Let's assume the width of the rectangle is "w" (in feet).
Since the length is twice the width, the length of the rectangle would be "2w" (in feet).
The formula to calculate the perimeter of a rectangle is P = 2l + 2w, where P represents the perimeter, l represents the length, and w represents the width.
Given that Brian has 96 feet of fencing, we can set up the equation:
96 = 2(2w) + 2w
Let's simplify this equation to solve for the width of the rectangle:
96 = 4w + 2w
Combining like terms, we get:
96 = 6w
To solve for w (width), we divide both sides of the equation by 6:
w = 96/6
w = 16
Therefore, the width of the rectangle is 16 feet.
Since the length is twice the width, the length would be:
l = 2w
l = 2(16)
l = 32
Therefore, the dimensions of the rectangle are:
Width = 16 feet
Length = 32 feet