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 36 meters, find the length of each side. note that x meters, 1.5x meters, 1.5x meters, x meters, x meters. the figure is not to the scale.

Explanation:

Step1: Set up perimeter equation

The perimeter of the pentagon is the sum of its side - lengths. The side - lengths are \(x\), \(x\), \(x\), \(1.5x\), \(1.5x\). So the perimeter \(P=x + x+x + 1.5x+1.5x\).
\[P=(1 + 1+1 + 1.5+1.5)x=6x\]

Step2: Solve for \(x\)

We know that \(P = 36\) meters. Substitute \(P = 36\) into the equation \(6x=36\).
\[x=\frac{36}{6}=6\]

Step3: Find side - lengths

For sides of length \(x\), the length is \(6\) meters.
For sides of length \(1.5x\), substitute \(x = 6\) into \(1.5x\), we get \(1.5\times6 = 9\) meters.

Answer:

The sides of length \(x\) are \(6\) meters and the sides of length \(1.5x\) are \(9\) meters.