Final answer:
The side length of the pentagon is 12 inches and the side length of the triangle is 20 inches. None of the above are correct.
Step-by-step explanation:
To find the side length of the pentagon and the triangle, let's start by setting up equations based on the given information. Let the side length of the pentagon be 'x' inches. This means the side length of the triangle is 'x + 8' inches. Since the pentagon is a regular pentagon, all of its sides have the same length.
The perimeter of the pentagon is 5 times the length of one side.
So, the perimeter of the pentagon is 5x inches. The perimeter of the equilateral triangle is 3 times the length of one side. So, the perimeter of the triangle is 3(x + 8) inches.
We can set up an equation: 5x = 3(x + 8). Now, we can solve for x:
Expand the equation: 5x = 3x + 24.
Combine like terms: 2x = 24.
Divide both sides by 2: x = 12.
Therefore, the side length of the pentagon is 12 inches. And since the side length of the triangle is 'x + 8', the side length of the triangle is 12 + 8 = 20 inches. The correct answer is none of these.