The perimeter of a rectangle is
72 feet. The length of the rectangle is twice the width. Find the length and width of the rectangle.
L = 2W
2L + 2W = 72
L + W = 36
2W + W = 36
3W = 36
W = 12 ----> L = 24
The rectangle is 24 ft long and 12 feet wide
check:
perimeter = 24+24+12+12 = 72
Let's say the width of the rectangle is "x" feet.
Since the length of the rectangle is twice the width, the length would be "2x" feet.
The formula for the perimeter of a rectangle is 2(length + width).
So, the perimeter would be:
2(2x + x) = 72
Simplifying the equation, we have:
2(3x) = 72
6x = 72
Dividing both sides by 6, we get:
x = 12
Therefore, the width of the rectangle is 12 feet.
The length of the rectangle is twice the width, so the length would be:
2 * 12 = 24 feet.
Hence, the length of the rectangle is 24 feet and the width is 12 feet.
To find the length and width of the rectangle, we can start by setting up equations based on the given information.
Let's assume the width of the rectangle is represented by the variable "w". As given, the length of the rectangle is twice the width, so it can be represented as "2w".
The formula for the perimeter of a rectangle is P = 2(l + w), where P is the perimeter, l is the length, and w is the width.
Given that the perimeter is 72 feet, we can substitute the values into the equation:
72 = 2(2w + w)
Simplifying, we have:
72 = 2(3w)
72 = 6w
To solve for w, we divide both sides of the equation by 6:
w = 12
So, the width of the rectangle is 12 feet.
Now, we can find the length of the rectangle by substituting w back into our expression for the length:
l = 2w
l = 2(12)
l = 24
Therefore, the length of the rectangle is 24 feet.
To summarize, the length of the rectangle is 24 feet and the width of the rectangle is 12 feet.
So if P=72ft , let's find an equation to compare! Perimeter=(Length x 2)+(width x 2) but we know that the length is twice the width or 2L=w , so let's substitute this back into our equation, P=(2L)(2w)=(2L)(2(2L))=8L^2=72
L^2=9
L=+-3 but it doesn't make sense to have a negative length so L must be 3. Plugging this back in, we get that 2L=w so w=6