Question

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 18 centimeters.
a. write an equation for perimeter.
b. solve the equation in part (a).
c. find the length of each side
a. choose the correct answer below.
a. x + x + x + x + x = 18
b. x + x + x + 3x + 3x = 18
c. x + x + x + 3x + 3x = 9
d. 9x = 18
b. x = (simplify your answer.)
c. each of the shorter sides has a length of cm. (simplify your answer.)
each of the longer sides has a length of cm. (simplify your answer.)

Explanation:

Step1: Write perimeter equation

The pentagon has three sides of length $x$ and two sides of length $3x$. The perimeter is the sum of all side - lengths, so the equation is $x + x+x + 3x+3x=18$.

Step2: Simplify the left - hand side

Combining like terms, we get $(1 + 1+1 + 3+3)x=9x$. So the equation becomes $9x = 18$.

Step3: Solve for $x$

Divide both sides of the equation $9x = 18$ by 9. We have $x=\frac{18}{9}=2$.

Step4: Find side lengths

The shorter sides have length $x$. Since $x = 2$, the length of each shorter side is 2 cm. The longer sides have length $3x$. Substituting $x = 2$ into $3x$, we get $3\times2 = 6$ cm.

Answer:

a. B. $x + x+x + 3x+3x=18$
b. $2$
c. Each of the shorter sides has a length of $2$ cm. Each of the longer sides has a length of $6$ cm.