Question

the perimeter of a geometric figure is the sum of the lengths of its sides. if the perimeter of the pentagon (five - sided figure) to the right is 32 meters, find the length of each side. note that the figure is not to the scale. 2.5x meters 2.5x meters x meters x meters x meters

Explanation:

Step1: Set up perimeter equation

The perimeter of a pentagon is the sum of its side - lengths. The side - lengths of the pentagon are \(x,x,2.5x,x,2.5x\). So the perimeter \(P=x + x+2.5x+x + 2.5x\). Combine like terms: \(P=(1 + 1+2.5 + 1+2.5)x=8x\).

Step2: Solve for \(x\)

We know that \(P = 32\) meters. Since \(P = 8x\), then \(8x=32\). Divide both sides of the equation by 8: \(x=\frac{32}{8}=4\) meters.

Step3: Find the length of each side

• For the sides with length \(x\): The length is 4 meters.
• For the sides with length \(2.5x\): Substitute \(x = 4\) into \(2.5x\), we get \(2.5\times4 = 10\) meters.

Answer:

The sides of length \(x\) are 4 meters each, and the sides of length \(2.5x\) are 10 meters each.