The length of a rectangle is two inches more than eight times the width. The perimeter is 166 inches. Find the length and width.
2(w + 8w+2) = 166
find w, and then the length
To find the length and width of the rectangle, we can use the information given and set up equations based on the given conditions.
Let's assume the width of the rectangle as "x" inches.
According to the problem, the length of the rectangle is two inches more than eight times the width, which can be expressed as 8x + 2.
The perimeter of a rectangle is given by the formula 2(length + width), which in this case is 2(8x + 2 + x) = 166 inches.
Simplifying the equation, we get:
2(9x + 2) = 166
Now, let's solve the equation to find the value of x:
First, distribute the 2:
18x + 4 = 166
Next, subtract 4 from both sides:
18x = 162
Finally, divide both sides by 18:
x = 9
Hence, the width of the rectangle is 9 inches.
To find the length, substitute x = 9 into the expression for the length:
Length = 8x + 2 = 8(9) + 2 = 74
Therefore, the length of the rectangle is 74 inches.
In conclusion, the width of the rectangle is 9 inches, and the length is 74 inches.