the length of a rectangle is 2 inches less than 8 times the width. the perimeter is 194 inches..find dimensions

P = 2L + 2W

194 = 2(8W - 2) + 2W

194 = 18W - 4

198 = 18W

11 = W

To find the dimensions of the rectangle, we can use the information provided about the length and width of the rectangle, as well as the perimeter.

Let's start by assigning variables to the dimensions of the rectangle:
- Let's say the width of the rectangle is "w" inches.
- According to the given information, the length of the rectangle is "8w - 2" inches.

To find the perimeter, we add up all lengths of the sides:
Perimeter = 2(length + width)

In this case, the perimeter is given as 194 inches, so we can set up the following equation:
194 = 2((8w - 2) + w)

Now, let's solve for "w" by simplifying and solving the equation step by step:

194 = 2(8w - 2 + w)
194 = 2(9w - 2) (Combine like terms)
194 = 18w - 4 (Distribute 2 to the terms inside the parentheses)
194 + 4 = 18w (Add 4 to both sides)
198 = 18w (Simplify)

Now, divide both sides of the equation by 18 to solve for "w":
198/18 = w
11 = w

So, the width of the rectangle is 11 inches.

To find the length, we substitute the value of the width we found (w = 11) into the expression for the length:
Length = 8w - 2
Length = 8(11) - 2
Length = 88 - 2
Length = 86

Therefore, the dimensions of the rectangle are:
Width = 11 inches
Length = 86 inches