The width of a rectangle is 6 cm less than the length. A second rectangle, with a perimeter of 54 cm, is 3 cm wider and 2 cm shorter than the first. What are the dimensions of each rectangle. Please give complete answer :)

1ST Rectangle

Length = x cm
Width = (x - 6) cm

2nd Rectangle

Perimeter = 54 cm
Width = (x - 6) + 3 = (x - 3) cm
Length = (x - 2) cm
P = 2W + 2L
P = 2(X - 3) + 2(X - 2)
54 = 2x - 6 + 2x - 4
x = 16 cm
Width = x - 3 = 16 - 3 = 13 cm
Length = x - 2 = 16 - 2 = 14 cm

1st Rectangle

Width = x - 6 = 16 - 6 = 10 cm
Length = x = 16 cm

To solve this problem, we need to break it down into steps and define variables for the unknowns.

Step 1: Define variables
Let's assume that the length of the first rectangle is 'L' cm, and the width is 'W' cm.

Step 2: Understand the problem
According to the problem, the width of the first rectangle is 6 cm less than the length. So, we can write the equation: W = L - 6.

Step 3: First Rectangle dimensions
The perimeter of a rectangle is given by the formula: P = 2(L + W). Since the perimeter of the first rectangle is not provided, we cannot determine its dimensions directly.

Step 4: Understand the second rectangle
The second rectangle is described as being 3 cm wider and 2 cm shorter than the first rectangle. So the length of the second rectangle can be represented as L + 3, and the width can be represented as W - 2.

Step 5: Equations for the second rectangle
Using the perimeter formula, we can set up the equation for the second rectangle: 54 = 2(L + 3 + W - 2).

Step 6: Solve for the second rectangle
Simplifying the equation: 54 = 2(L + W + 1).
Dividing by 2: 27 = L + W + 1.
Rearranging terms: L + W = 26.

Step 7: Substitute the value of W
We already know that W = L - 6, so we can substitute this expression into the equation from step 6: L + (L - 6) = 26.

Step 8: Solve for L
Simplifying the equation: 2L - 6 = 26.
Adding 6 to both sides: 2L = 32.
Dividing by 2: L = 16.

Step 9: Calculate the dimensions of the first rectangle
Using the value of L, we can substitute it into the equation W = L - 6: W = 16 - 6 = 10.
So, the dimensions of the first rectangle are length = 16 cm and width = 10 cm.

Step 10: Calculate the dimensions of the second rectangle
The length of the second rectangle is L + 3 = 16 + 3 = 19 cm.
The width of the second rectangle is W - 2 = 10 - 2 = 8 cm.
So, the dimensions of the second rectangle are length = 19 cm and width = 8 cm.

Therefore, the dimensions of each rectangle are as follows:
First Rectangle: Length = 16 cm, Width = 10 cm.
Second Rectangle: Length = 19 cm, Width = 8 cm.