The length of a rectangle is two more than three times its width. Find the dimensions of the rectangle if the perimeter is twenty meters.
P = 2L + 2W
20 = 2(3W + 2) + 2W
20 = 6W + 4 + 2W
16 = 8W
2 = W
To solve this problem, we can start by defining the variables given in the question:
Let's say the width of the rectangle is represented by 'w'.
So, the length of the rectangle is 3w + 2.
The formula for the perimeter of a rectangle is:
Perimeter = 2 * (Length + Width)
According to the question, the perimeter is 20 meters. Substituting the values we have, we get:
20 = 2 * (w + 3w + 2)
Simplifying the equation:
20 = 2 * (4w + 2)
20 = 8w + 4
16 = 8w
w = 16 / 8
w = 2
Now that we have the width (w = 2), we can find the length by substituting w into our expression for the length:
Length = 3w + 2
Length = 3 * 2 + 2
Length = 6 + 2
Length = 8
Therefore, the dimensions of the rectangle are:
Width = 2 meters
Length = 8 meters