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 28 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 = 7 b. x + x + x + 2x + 2x = 28 c. 4x^5 = 28 d. x + x + x + x + x = 28 b. x = 4 (simplify your answer.) c. the shorter sides have a length of cm. (simplify your answer.)

Explanation:

Step1: Identify the perimeter equation

We know from part (a) the correct perimeter - equation is \(x + x+x + 2x+2x=28\), which simplifies to \(7x = 28\) (by combining like - terms: \(1x+1x + 1x+2x + 2x=(1 + 1+1 + 2+2)x=7x\)).

Step2: Solve for \(x\)

Given the equation \(7x = 28\), we divide both sides of the equation by 7. Using the formula \(\frac{7x}{7}=\frac{28}{7}\), we get \(x = 4\).

Step3: Find the length of the shorter sides

The shorter sides are represented by \(x\). Since \(x = 4\), the length of the shorter sides is 4 cm.

Answer:

a. B. \(x + x+x + 2x+2x=28\)
b. \(x = 4\)
c. 4