A rectangle has a perimeter of 110 inches. The width of the rectangle is 9 inches less than the length; what is the width, in inches, of the rectangle?
2(w + w+9) = 110
Let's assume the length of the rectangle is x inches.
According to the given information, the width of the rectangle is 9 inches less than the length. So, the width can be expressed as x - 9 inches.
The perimeter of a rectangle is calculated by adding the lengths of all four sides. In this case, the perimeter is given as 110 inches.
Since a rectangle has two pairs of equal sides, the perimeter can also be calculated as twice the sum of the length and width.
Using this information, we can write the equation:
2(length + width) = 110
Substituting the expressions for length and width, we get:
2(x + x - 9) = 110
Simplifying the equation:
2(2x - 9) = 110
4x - 18 = 110
4x = 128
x = 32
So, the length of the rectangle is 32 inches.
Now, substituting the value of x into the expression for width:
width = x - 9
width = 32 - 9
width = 23
Therefore, the width of the rectangle is 23 inches.
To find the width of the rectangle, let's first define the variables. Let's say the length of the rectangle is L inches, and the width of the rectangle is W inches.
According to the given information, we know that the width of the rectangle is 9 inches less than the length. So we can write the equation:
W = L - 9
Now, we are also given that the perimeter of the rectangle is 110 inches. The formula for the perimeter of a rectangle is:
Perimeter = 2 * (Length + Width)
By substituting the values of length and width into the formula, we can write the equation:
110 = 2 * (L + W)
Now we can substitute the value of W from the first equation into the second equation:
110 = 2 * (L + (L - 9))
Simplifying further:
110 = 2 * (2L - 9)
Distributing and simplifying again:
110 = 4L - 18
Adding 18 to both sides:
128 = 4L
Dividing both sides by 4:
L = 32
So the length of the rectangle is 32 inches. Now we can substitute this value into the first equation to find the width:
W = 32 - 9
W = 23
Therefore, the width of the rectangle is 23 inches.