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 140 meters, find the length of each side. note that the figure is not to the scale. x meters x meters x meters 3.5x meters 3.5x meters

Explanation:

Step1: Set up perimeter equation

The perimeter of the pentagon is the sum of its side - lengths. The side - lengths are \(3.5x,3.5x,x,x,x\). So the perimeter \(P=3.5x + 3.5x+x+x+x\).
Combining like terms, \(P=(3.5 + 3.5+1 + 1+1)x=10x\).

Step2: Solve for \(x\)

We know that \(P = 140\) meters. Since \(P = 10x\), we set up the equation \(10x=140\).
Dividing both sides by 10, we get \(x=\frac{140}{10}=14\).

Step3: Find \(3.5x\)

Substitute \(x = 14\) into \(3.5x\). Then \(3.5x=3.5\times14 = 49\).

Answer:

\(x = 14\)
\(3.5x=49\)