The width of a rectangle is w yards and the length of the rectangle is(5w-8) yards. The perimeter of the rectangle is given by the algebraic expression 2w +2. Simplify the algebraic expression 2w + 2(5w--8) and determine the perimeter of a rectangle whose width w is 6 yards.
To simplify the expression 2w + 2(5w - 8), you can distribute the 2 across the expression inside the parentheses:
2w + 2(5w) + 2(-8)
= 2w + 10w + (-16)
= 12w - 16
To find the perimeter of a rectangle with a width of 6 yards, substitute w = 6 into the simplified expression:
12w - 16
= 12(6) - 16
= 72 - 16
= 56
Therefore, the perimeter of a rectangle with a width of 6 yards is 56 yards.
To simplify the expression 2w + 2(5w - 8), we distribute the 2 to both terms inside the parentheses:
2w + 2(5w - 8) = 2w + 10w - 16
Next, we combine like terms:
2w + 10w - 16 = 12w - 16
So the simplified expression is 12w - 16.
To determine the perimeter of a rectangle with a width of 6 yards, we substitute w = 6 into the expression 12w - 16:
Perimeter = 12w - 16
Perimeter = 12(6) - 16
Perimeter = 72 - 16
Perimeter = 56 yards
Therefore, the perimeter of the rectangle with a width of 6 yards is 56 yards.