The length of a rectangle is 2 1/2 times the width, and the perimeter is 42 feet. What are the dimensions of this rectangle?
P = 2L + 2W
42 = 2(2.5W) + 2W
42 = 5W + 2W
42 = 7W
6 = W
Let's call the width of the rectangle "w".
According to the given information, the length of the rectangle is 2 1/2 times the width. Therefore, the length can be expressed as 2 1/2 * w.
The perimeter of a rectangle is calculated by adding up the lengths of all four sides. In this case, it is given to be 42 feet.
Since we have the formula for the perimeter (P) of a rectangle, which is P = 2 * (length + width), we can substitute the values:
42 = 2 * ((2 1/2 * w) + w)
Now we solve for w:
42 = 2 * (5/2 * w + w)
42 = 2 * (7/2 * w)
Divide both sides by 2:
21 = 7/2 * w
Multiply both sides by 2/7:
w = (21 * 2) / 7
w = 6
So, the width of the rectangle is 6 feet.
To find the length of the rectangle, we substitute the width value back into the equation for the length:
Length = 2 1/2 * w
= 2 1/2 * 6
= (2 * 6 + 6/2)
= (12 + 3)
= 15
Therefore, the dimensions of the rectangle are 6 feet by 15 feet.
To find the dimensions of the rectangle, we can use the given information about the length, width, and perimeter.
Let's assume the width of the rectangle is "w" feet. According to the problem, the length is 2 1/2 times the width, which can be expressed as:
Length = 2 1/2 * Width
Length = 5/2 * Width
Length = (5/2)w
The perimeter of a rectangle is given by the formula:
Perimeter = 2 * (Length + Width)
Substituting the values we know, we can write:
42 = 2 * ((5/2)w + w)
Now, let's solve this equation to find the value of "w" (width):
42 = 2 * ((5/2)w + w)
42 = 2 * ((5w/2) + 2w/2)
42 = 2 * (7w/2)
42 = 7w
Now, we can solve for "w":
w = 42/7
w = 6 feet
So, the width of the rectangle is 6 feet.
To find the length, we can substitute the value of "w" back into the equation for length:
Length = (5/2)w
Length = (5/2) * 6
Length = 15 feet
Therefore, the width of the rectangle is 6 feet, and the length is 15 feet.