Short Answer 
The perimeter of the rectangle is calculated to be 38 cm by determining its dimensions from the areas of associated squares, resulting in a length of 12 cm and a width of 7 cm.
Step 1: Define the Shapes and Variables
First, we establish the shapes and their corresponding variables. The large square can be represented as having an area of y + 95 while the smaller square has an area of y. The rectangle has a width of x and a length of x + 5, where x represents the width of the smaller square.
Step 2: Set Up the Area Equations
Next, we create the area equations based on the definitions from Step 1. The area of the large square can be expressed as:
- (x + 5)² = y + 95
- x² = y
By substituting the second equation into the first, we can simplify and solve for x and y.
Step 3: Calculate Perimeter of the Rectangle
After solving, we find that x = 7 and y = 49. Now we can determine the dimensions of the rectangle:
- Length = x + 5 = 12
- Width = x = 7
Finally, we compute the perimeter of the rectangle using the formula Perimeter = 2(length) + 2(width), which results in:
- Perimeter = 2(12) + 2(7) = 38 cm