the length of a rectangle is 4 less than 3 times the width if the perimeter is 48 inches find the length and the width
2(w + 3w-4) = 48
find w, and then you can get the length.
To find the length and width of the rectangle, we can use the given information about the relationship between the length and width as well as the perimeter.
Let's represent the width of the rectangle as 'w' (in inches) and the length as 'l' (in inches).
According to the given information, the length of the rectangle is 4 less than 3 times the width, which can be written as:
l = 3w - 4
The perimeter of a rectangle is calculated by adding the lengths of all sides. For a rectangle, since opposite sides are equal in length, the perimeter can be calculated using the formula:
Perimeter = 2(length) + 2(width)
For our rectangle, the perimeter is given as 48 inches, so we can write the equation as:
48 = 2l + 2w
Now we have a system of two equations:
l = 3w - 4
48 = 2l + 2w
To solve this system of equations, we can substitute the value of 'l' from the first equation into the second equation:
48 = 2(3w - 4) + 2w
Let's simplify and solve for 'w':
48 = 6w - 8 + 2w
48 = 8w - 8
56 = 8w
w = 7
Now that we have the value of 'w', we can substitute it back into the first equation to find the value of 'l':
l = 3w - 4
l = 3(7) - 4
l = 21 - 4
l = 17
Therefore, the width of the rectangle is 7 inches and the length is 17 inches.