Final answer:
The perimeter of the pentagon is 45 inches and the perimeter of the triangle is also 45 inches.
Step-by-step explanation:
The perimeter of a regular pentagon is given by the formula P = 5s, where s is the length of each side. In this case, the perimeter of the pentagon is 5(1/2x - 1) inches.
The perimeter of an equilateral triangle is given by the formula P = 3s, where s is the length of each side. In this case, the perimeter of the triangle is 3(x - 5) inches.
To find the values of x and the perimeters of each figure, we can set the two expressions equal to each other:
5(1/2x - 1) = 3(x - 5)
Next, we solve for x:
2.5x - 5 = 3x - 15
Adding 5 to both sides:
2.5x = 3x - 10
Subtracting 3x from both sides:
-0.5x = -10
Dividing both sides by -0.5:
x = 20
Now we can substitute x = 20 into the expressions for the perimeters to find the actual values:
Perimeter of pentagon = 5(1/2(20) - 1) = 5(10 - 1) = 45 inches
Perimeter of triangle = 3(20 - 5) = 3(15) = 45 inches