The length of a rectangle is 3 feet less than 4 times the width. If the perimeter is 84 feet, find the length and the width of the rectangle.
L + w = 42
L + 3 = 4 w
42 - w + 3 = 4 w
5 w = 45 etc
P = 2L + 2W
84 = 2(4W - 3) + 2W
84 = 10W - 6
90 = 10W
9 = W
9x4-3=33 l
To find the length and width of the rectangle, we need to set up a system of equations based on the given information.
Let "x" be the width of the rectangle.
According to the problem, the length of the rectangle is 3 feet less than 4 times the width, which can be expressed as (4x - 3).
The perimeter of a rectangle is calculated by adding up the lengths of all its sides. In this case, we have two sides of length x and two sides of length (4x - 3). Therefore, the perimeter equation is:
Perimeter = 2x + 2(4x - 3) = 84
Now we can solve the equation to find the value of x, which will give us the width of the rectangle.
2x + 8x - 6 = 84
10x - 6 = 84
10x = 90
x = 9
The width of the rectangle is 9 feet.
To find the length, we substitute the value of x back into the expression we derived earlier:
Length = 4x - 3
Length = 4(9) - 3
Length = 36 - 3
Length = 33
The length of the rectangle is 33 feet.
Therefore, the width of the rectangle is 9 feet and the length is 33 feet.