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. x + x + x + 2x + 2x = 1
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 4 cm. (simplify your answer.)
the longer sides have a length of cm. (simplify your answer)

Explanation:

Step1: Identify the equation for perimeter

The perimeter of a figure is the sum of side - lengths. Given side - lengths \(x,x,x,2x,2x\) and perimeter \(28\), the equation is \(x + x+x + 2x+2x=28\).

Step2: Combine like - terms

Combining the \(x\) terms on the left - hand side, we have \((1 + 1+1 + 2+2)x=28\), which simplifies to \(7x = 28\).

Step3: Solve for \(x\)

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

Step4: Find the length of the longer sides

The longer sides are of length \(2x\). Substituting \(x = 4\) into \(2x\), we get \(2\times4 = 8\).

Answer:

a. B. \(x + x+x + 2x+2x=28\)
b. \(x = 4\)
c. The shorter sides have a length of \(4\) cm. The longer sides have a length of \(8\) cm.