The plans for a she'd call for a rectangular floor with a perimeter of 276ft. The length is two times the width. Find the length and the width
L = 2 W
P = 2 L + 2 W = 2 ( L + W )
276 = 2 ( L + W )
276 = 2 ( 2 W + W )
276 = 2 * 3 W
276 = 6 W Diwide both sides by 6
46 = W
W = 46 ft
L = 2 W = 2 * 46 = 92 ft
Proof:
P = 2 ( W + L ) = 2 * ( 46 + 92 ) = 2 * 138 = 276 ft
Let's represent the width of the shed as "w" feet.
Since the length is two times the width, we can represent the length as "2w" feet.
The perimeter of a rectangle is calculated by adding all the sides.
In this case, the formula for the perimeter is:
Perimeter = 2 * (Length + Width)
So, for this shed, the perimeter is:
276 = 2 * (2w + w)
Simplifying the equation:
276 = 2 * (3w)
Divide both sides of the equation by 2:
138 = 3w
Finally, divide both sides of the equation by 3 to solve for "w":
w = 138 / 3
w ≈ 46
The width of the shed is approximately 46 feet.
To find the length, substitute the value of the width back into the equation for length:
Length = 2w
Length = 2 * 46
Length ≈ 92
The length of the shed is approximately 92 feet.
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 the width of the shed is 'w' feet. According to the problem, the length is two times the width, so the length would be '2w' feet.
We know that the perimeter of a rectangle is the sum of all its sides. In this case, the perimeter is given as 276 feet.
Therefore, the perimeter of the shed can be expressed as:
2 * (length + width) = 276
Substituting the values for length and width in terms of 'w' into the equation above, we get:
2 * (2w + w) = 276
Simplifying the equation:
2 * (3w) = 276
6w = 276
w = 276/6
w = 46
So, the width of the shed is 46 feet.
Since the length is two times the width, we can calculate the length as:
length = 2 * width = 2 * 46 = 92
Therefore, the length of the shed is 92 feet.
In conclusion, the width of the shed is 46 feet and the length is 92 feet.