Question

the perimeter of a geometric figure is the sum of the lengths of its sides. a pentagon (five - sided figure) on the right is 36 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 + 3x + 3x = 9 b. 9x^5 = 36 c. x + x + x + x + x = 36 d. x + x + x + 3x + 3x = 36 b. x = (simplify your answer.)

Explanation:

Step1: Combine like - terms in the equation

The equation for the perimeter is $x + x+x + 3x+3x=36$. Combining like - terms on the left - hand side gives $(1 + 1+1 + 3+3)x=9x$. So the equation becomes $9x = 36$.

Step2: Solve for $x$

Divide both sides of the equation $9x = 36$ by 9. We have $\frac{9x}{9}=\frac{36}{9}$, which simplifies to $x = 4$.

Step3: Find the length of each side

The side lengths are $x,x,x,3x,3x$. Substituting $x = 4$:

• The three sides of length $x$ have length 4 cm each.
• The two sides of length $3x$ have length $3\times4 = 12$ cm each.

Answer:

a. D. $x + x+x + 3x+3x=36$
b. $x = 4$
c. Three sides are 4 cm each and two sides are 12 cm each.