The perimeter of a recatngles is 54 inches. THe width is one inch less than the length.
FInd the length and width
If the length is x, then
2(x-1 + x) = 54
2x-2+2x=54
4xx-2=54-2
4x/4 = 52/4
x=13
To find the length and width of the rectangle, we can set up two equations based on the given information.
Let's assume that the length of the rectangle is L inches. Then, according to the problem, the width will be one inch less than the length, so the width can be represented as (L - 1) inches.
We know that the perimeter of a rectangle is calculated by adding up all its sides, which in this case is equal to 54 inches.
The formula for the perimeter of a rectangle is given by:
Perimeter = 2 * (Length + Width)
So we can set up the following equation:
54 = 2 * (L + (L - 1))
Now, let's solve the equation to find the length and width of the rectangle.
1. Expand and simplify the equation:
54 = 2 * (2L - 1)
2. Distribute the 2 to both terms inside the parentheses:
54 = 4L - 2
3. Move the constant term to the other side of the equation by adding 2 to both sides:
54 + 2 = 4L
4. Simplify the left side:
56 = 4L
5. Divide both sides by 4 to isolate L:
56/4 = L
L = 14
Therefore, the length of the rectangle is 14 inches.
Now, let's find the width by substituting the value of L in the equation for the width:
Width = L - 1
Width = 14 - 1
Width = 13
Therefore, the width of the rectangle is 13 inches.
To recap, the length of the rectangle is 14 inches, and the width is 13 inches.