The perimeter of a geometric figure is the sum of the lengths of its sides. The perimeter of the pentagon (five-sided figure) on the right is 45 centimeters.

a. Write an equation for the perimeter.
b. Solve the equation in part (a).
c. Find the length of each side.

A. [tex]x + x + x + 3x + 3x = 45[/tex]
B. [tex]x + x + x + 3x + 3x = 9[/tex]
C. [tex]9x^5 = 45[/tex]
D. [tex]x + x + x + x + x = 45[/tex]

Let's solve the problem step-by-step.

a. Write an equation for the perimeter:

The problem states that the pentagon's perimeter is the sum of its side lengths, which equals 45 centimeters. In this case, the sides are given as three sides of length [tex]$ x $[/tex] and two sides of length [tex]$ 3x $[/tex]. So, we can write the equation for the perimeter as:
[tex]\[ x + x + x + 3x + 3x = 45 \][/tex]

b. Solve the equation:

Let's simplify the equation:
[tex]\[ 3x + 6x = 45 \][/tex]

When simplified, this equation becomes:
[tex]\[ 9x = 45 \][/tex]

To find the value of [tex]$ x $[/tex], divide both sides of the equation by 9:
[tex]\[ x = \frac{45}{9} \][/tex]
[tex]\[ x = 5 \][/tex]

c. Find the length of each side:

Now that we know [tex]$ x = 5 $[/tex], let's find the length of each side:

- The first three sides are each [tex]$ x $[/tex], which means they are [tex]$ 5 $[/tex] centimeters long.
- The last two sides are each [tex]$ 3x $[/tex], so they are [tex]$ 3 \times 5 = 15 $[/tex] centimeters long.

So, the side lengths of the pentagon are:
- Three sides measuring 5 centimeters each.
- Two sides measuring 15 centimeters each.