The plans for a shed call for a rectangular floor with a perimeter of 192 ft. The length is two times the width. Find the length and width.
The width is ____ft
The length is ____ ft
p = 2 L + 2 w
192 = 2 L + 2 w
L = 2 w
so
192 = 2 (2w) + 2 w
192 = 6 w
w = 32 etc
P = 2L + 2W
192 = 2W + 2(2W)
192 = 6W
32 = W
To find the length and width of the shed, we can set up a system of equations based on the given information.
Let's assume that the width of the shed is denoted as "w" (in ft).
Given that the length is two times the width, we can express the length as "2w" (in ft).
The perimeter of a rectangle can be calculated by adding the lengths of all four sides. For a rectangle, opposite sides are equal in length. So, we can write the equation for the perimeter as:
Perimeter = 2(length + width)
Substituting the given values into the equation, we have:
192 ft = 2(2w + w)
Now, let's solve this equation to find the value of "w."
First, simplify the right side of the equation:
192 ft = 2(3w)
Next, distribute the 2:
192 ft = 6w
To isolate "w," divide both sides of the equation by 6:
192 ft ÷ 6 = 6w ÷ 6
32 ft = w
Therefore, the width of the shed is 32 ft.
To find the length, we can substitute the value of "w" back into the equation for length:
Length = 2w
Length = 2(32 ft)
Length = 64 ft
Therefore, the length of the shed is 64 ft.