The variable W represents the width of a rectangle. The length of the rectangle, L, is 5 less than twice the width.
Write an expression for the length of the rectangle in terms of W.
Write a simplified expression for the perimeter of the rectangle in terms of W.
Find the perimeter of the rectangle if the width is 3 inches.
Well W = 3
L = (2W)-5 = (6) - 5 = 1
so
W + W + L + L = perimeter
so 2W + 2L = perimeter
so subbing 2W-5 in for L we get
2W + 2(2W-5) = perimeter
= 2W + 4W-10 = perimeter
= 6W - 10 = perimeter
= 6(3) - 10 = perimeter
=18 - 10 = perimeter
= 8 = perimeter
or solving the other way L = 1 W = 3
2W + 2L = 6 + 2 = 8 = perimeter
1. To find an expression for the length of the rectangle in terms of W, we first need to understand the relationship described. The length L is given as 5 less than twice the width W.
Therefore, we can write the expression for the length of the rectangle in terms of W as:
L = 2W - 5.
2. To find a simplified expression for the perimeter of the rectangle in terms of W, we need to remember that the perimeter of a rectangle is calculated by adding all four sides. In this case, the length and width of the rectangle are variable, represented by L and W respectively.
Therefore, the perimeter P can be calculated as:
P = 2(L + W).
Replacing the expression for L from step 1, we get:
P = 2((2W - 5) + W).
3. To find the perimeter of the rectangle when the width is 3 inches, we can substitute W = 3 into the expression obtained in step 2.
P = 2((2(3) - 5) + 3).
Simplifying, we get:
P = 2(6 - 5 + 3).
Further simplifying, we get:
P = 2(4) = 8.
Therefore, the perimeter of the rectangle is 8 inches when the width is 3 inches.
To find the length of the rectangle in terms of W, we know that L is 5 less than twice the width. So, we can write the expression as:
L = 2W - 5
To find the perimeter of the rectangle in terms of W, we need to add up all the sides of the rectangle. The rectangle has two lengths and two widths, so the perimeter would be:
P = 2L + 2W
Now, let's substitute the expression for L into the perimeter equation:
P = 2(2W - 5) + 2W
P = 4W - 10 + 2W
P = 6W - 10
To find the perimeter of the rectangle if the width is 3 inches, we can plug in W = 3 into the expression for the perimeter:
P = 6(3) - 10
P = 18 - 10
P = 8 inches
Therefore, the perimeter of the rectangle with a width of 3 inches is 8 inches.