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.

Answer 1

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.