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.

Answer 1

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.