The length of a rectangle is 9 inches more than the width. If the perimeter is 110 inches, what are the length and the width?
Length=
Width=
2(w + w+9) = 110
To find the length and width of a rectangle given its perimeter, you can use the perimeter formula.
Let's denote:
L = Length of the rectangle
W = Width of the rectangle
From the problem statement, we know that the length is 9 inches more than the width. So, we can say that:
L = W + 9
The perimeter of a rectangle is the sum of all its sides, which can be calculated using the formula:
Perimeter = 2(L + W)
Given that the perimeter is 110 inches, we can substitute the values into the formula:
110 = 2(L + W)
Now, we can substitute the expression we found for L into the equation:
110 = 2((W + 9) + W)
Simplifying the equation:
110 = 2(2W + 9)
110 = 4W + 18
Now, let's solve for W by isolating it on one side of the equation. We'll start by subtracting 18 from both sides:
110 - 18 = 4W
92 = 4W
Finally, divide both sides by 4 to solve for W:
92/4 = W
23 = W
Therefore, the width of the rectangle is 23 inches.
To find the length of the rectangle, we can substitute this value back into the equation L = W + 9:
L = 23 + 9
L = 32
So, the length of the rectangle is 32 inches and the width is 23 inches.