A rectangle has a perimeter of 20 cm. The length of the rectangle is 1 more than twice the width. What is the measurement of the length and width of the rectangle?
P = 2L + 2W
20 = 2(2W + 1) + 2W
20 = 6W + 2
18 = 6W
3 = W
how did you substitute?
To find the length and width of the rectangle, let's assign variables to represent the unknowns. Let's use 'L' for the length and 'W' for the width.
According to the given information:
1. The perimeter of a rectangle is calculated by adding together the lengths of all its sides. In this case, the perimeter is given as 20 cm.
2. The length of the rectangle is 1 more than twice the width. So we can write this relationship as: L = 2W + 1.
To solve for the length and width, we need to set up an equation using the information provided.
The perimeter of a rectangle is calculated by adding the lengths of all its sides. In this case, the rectangle has two equal lengths (both of which are L) and two equal widths (both of which are W).
So, the equation for the perimeter can be written as:
2L + 2W = 20.
Now we can substitute the relationship between the length and width (L = 2W + 1) into the perimeter equation and solve for the values of L and W.
Substituting L = 2W + 1 in the perimeter equation:
2(2W + 1) + 2W = 20
4W + 2 + 2W = 20
6W + 2 = 20
6W = 20 - 2
6W = 18
W = 18/6
W = 3
Now that we have the width, we can substitute this value back into the relationship L = 2W + 1 to find the length.
L = 2(3) + 1
L = 6 + 1
L = 7
Therefore, the length of the rectangle is 7 cm and the width is 3 cm.