Question

A regular pentagon and an equilateral triangle have the same perimeter. The perimeter of the pentagon is 5(1/2 X-1) inches The perimeter of the triangle is 3(x-5) inches what is the perimeter of each figure

Answer 1

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