THe perimeter of a rectangle is 166 inches. The length exceeds the width by 23 inches. Find the lenght and the width
P = 2L + 2W
L = W + 23
166 = 2W + (2W + 46)
166 = 4W + 46
120 = 4W
30 = W
To find the length and width of the rectangle, we can set up two equations based on the given conditions.
Let's assume the width of the rectangle is "w" inches.
According to the given condition, the length exceeds the width by 23 inches, so the length can be represented as "w + 23" inches.
The perimeter of a rectangle is the sum of all sides:
Perimeter = 2 * (length + width)
In this case, the perimeter is given as 166 inches. Substituting the values, we get:
166 = 2 * (w + (w + 23))
Simplifying the equation:
166 = 2 * (2w + 23)
166 = 4w + 46
120 = 4w
w = 30
Substituting the value of "w" back into the equation for the length:
Length = w + 23
Length = 30 + 23
Length = 53
Therefore, the width of the rectangle is 30 inches, and the length is 53 inches.