The length of a rectangle is 2 more than 3 times its width. Find the dimensions of the rectangle if the perimeter is 44 in.
Let w = the width
Let 3w + 2 = the length
P = 2l + 2w
44 = 2(3w+2) + 2w
44 = 6w + 4 + 2w
44 = 8w + 4
40 = 8w
w = 5 feet
length - 3w + 2 = 3(5) + 2 = 15 + 2
l = 17 feet
L = 3W + 2
2L + 2W = 2(3W+2) + 2W = 44
Solve for W then L.
Let's start by setting up the information given:
Let's assume the width of the rectangle is "w" inches.
According to the given information, the length of the rectangle is 2 more than 3 times its width, which means the length is "3w + 2" inches.
The formula for the perimeter of a rectangle is: Perimeter = 2(length + width) or P = 2(l + w).
Given that the perimeter is 44 inches, we can set up the equation:
44 = 2(3w + 2 + w)
Now, let's simplify and solve for "w":
44 = 2(4w + 2)
44 = 8w + 4
40 = 8w
w = 5
Now that we have the width, we can find the length by substituting the value of "w" back into the equation for the length:
Length = 3w + 2
Length = 3(5) + 2
Length = 15 + 2
Length = 17
Therefore, the dimensions of the rectangle are a width of 5 inches and a length of 17 inches.
To find the dimensions of the rectangle, we can use the information given about its length and width, as well as the equation for the perimeter of a rectangle.
Let's start by assigning variables to the width and length of the rectangle. Let's say the width of the rectangle is 'w' and the length is 'L'.
According to the given information, the length of the rectangle is 2 more than 3 times its width, which can be expressed as:
L = 3w + 2
The equation for the perimeter of a rectangle is:
P = 2L + 2w
Substituting the value of L from the first equation into the perimeter equation, we have:
44 = 2(3w + 2) + 2w
Simplifying the equation, we get:
44 = 6w + 4 + 2w
Combining like terms, we have:
44 = 8w + 4
Subtracting 4 from both sides, we get:
40 = 8w
Dividing both sides by 8:
5 = w
So, the width of the rectangle is 5 inches.
Substituting this value back into the equation for the length of the rectangle, we have:
L = 3(5) + 2
L = 15 + 2
L = 17
Therefore, the dimensions of the rectangle are 5 inches for width and 17 inches for length.