The width of a rectangle is w yards and the length of the rectangle is (3w-4) yards. The perimeter of the rectangle is given by the algebraic expression 2w+2(3w-4). simplify the algebraic expression 2w+2(3w-4) and determine the perimeter of a rectangle whose width w is 2 yards.
To simplify the algebraic expression 2w + 2(3w - 4), we can distribute the 2 to both terms inside the parentheses:
2w + 2(3w - 4) = 2w + 6w - 8
Combining like terms, we get:
2w + 6w - 8 = 8w - 8
Therefore, the simplified algebraic expression is 8w - 8.
To determine the perimeter of a rectangle with width w = 2 yards, we can substitute w = 2 into the expression:
Perimeter = 8w - 8 = 8(2) - 8 = 16 - 8 = 8 yards.
Therefore, the perimeter of the rectangle is 8 yards.
To simplify the expression 2w + 2(3w - 4), we need to apply the distributive property.
First, distribute the 2 to both terms inside the parentheses:
2w + 2(3w - 4) = 2w + 6w - 8
Next, combine like terms:
2w + 6w - 8 = 8w - 8
So, the simplified algebraic expression is 8w - 8.
To find the perimeter of a rectangle with a width of 2 yards, substitute w = 2 into the expression:
Perimeter = 8w - 8
= 8(2) - 8
= 16 - 8
= 8
Therefore, the perimeter of the rectangle is 8 yards.
To simplify the algebraic expression 2w + 2(3w - 4), we need to simplify the terms inside parentheses first, and then combine like terms.
Step 1: Simplify the expression inside the parentheses
2w + 2(3w - 4)
= 2w + 2 * 3w - 2 * 4 (Apply the distributive property)
= 2w + 6w - 8 (Simplify inside parentheses)
= 8w - 8 (Combine like terms)
Now that we have simplified the expression, we can determine the perimeter of a rectangle with a width of 2 yards by substituting w = 2 into the simplified expression.
Perimeter = 8w - 8
Substitute w = 2
= 8 * 2 - 8
= 16 - 8
= 8 yards
Therefore, the perimeter of a rectangle with a width of 2 yards is 8 yards.