The length of a rectangle is 4 centimeters less than twice its width. The perimeter of the rectangle is 34 cm. What are the dimensions of the rectangle

To solve this problem, we can start by assigning variables to the unknown quantities mentioned in the question.

Let's say the width of the rectangle is 'w' centimeters. According to the problem, the length of the rectangle is 4 centimeters less than twice its width. So, the length can be expressed as 2w - 4.

The perimeter of a rectangle is given by the formula: P = 2w + 2l, where 'P' represents the perimeter, 'w' represents the width, and 'l' represents the length.

In this case, we know that the perimeter of the rectangle is 34 cm. Therefore, we can set up an equation:

34 = 2w + 2(2w - 4)

Now, let's solve this equation to find the value of 'w'.

34 = 2w + 4w - 8 (distributed the 2 to 2w and -4)
42 = 6w - 8 (combined like terms)
6w = 50 (added 8 to both sides)
w = 8.33 (divided both sides by 6)

Since the width of a rectangle cannot be 8.33 cm (as it is not a whole number), we need to round it to the nearest whole number. Therefore, the width is 8 cm.

To find the length, we can substitute the width value back into our expression for the length:
Length = 2w - 4 = 2(8) - 4 = 12 cm

So, the dimensions of the rectangle are:
Width = 8 cm
Length = 12 cm

P = 2L + 2W

34 = 2(2W - 4) + 2W
34 = 4W - 8 + 2W
34 = 6W - 8
42 = 6W
42/6 = W
7 = W

Length = ?