Final answer:
To find the perimeters of the pentagon and equilateral triangle, set up and solve equations for each figure's perimeter using the given information. Substitute the values of x back into the equations to find the perimeters.
Step-by-step explanation:
To find the perimeter of each figure, we need to set up and solve an equation. Let's start with the equation for the perimeter of the pentagon, which is given as 5(3x + 2) inches. Now, let's set up the equation for the perimeter of the equilateral triangle, which is 4(x - 2) inches. We can solve these equations to find the values of x, and then substitute those values back into the equations to find the perimeters of each figure.
Solving the equation for the pentagon's perimeter: 5(3x + 2) = perimeter of the pentagon
Solving the equation for the triangle's perimeter: 4(x - 2) = perimeter of the triangle
Once we have the values of x, we can substitute them back into the equations to find the perimeters of each figure.