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 14 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 + 2x + 2x = 14 b. 4x^5 = 14 c. x + x + x + 2x + 2x = 7 d. x + x + x + x + x = 14 b. x = (simplify your answer.) c. the shorter sides have a length of (simplify your answer.) the longer sides have a length of (simplify your answer.)

Explanation:

Step1: Write perimeter equation

The pentagon has three sides of length $x$ and two sides of length $2x$. The perimeter is the sum of all side - lengths, so $x + x+x + 2x+2x=14$. The correct answer for part (a) is A.

Step2: Combine like - terms

Combining the $x$ terms on the left - hand side of the equation $x + x+x + 2x+2x=14$, we get $(1 + 1+1 + 2+2)x=14$, which simplifies to $7x = 14$.

Step3: Solve for $x$

Dividing both sides of the equation $7x = 14$ by 7, we have $x=\frac{14}{7}=2$.

Step4: Find side lengths

The shorter sides have length $x$. Since $x = 2$, the shorter sides have length 2 centimeters. The longer sides have length $2x$. Substituting $x = 2$ into $2x$, we get $2\times2 = 4$ centimeters.

Answer:

a. A. $x + x+x + 2x+2x=14$
b. 2
c. The shorter sides have a length of 2 centimeters.
The longer sides have a length of 4 centimeters.