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

Explanation:

Step1: Set up perimeter equation

The perimeter $P$ of the pentagon is the sum of its side - lengths. So $P=x + x+x + 2.5x+2.5x$. Simplifying the right - hand side gives $P=(1 + 1+1 + 2.5+2.5)x=8x$.

Step2: Solve for $x$

We know that $P = 48$ meters. Substituting $P = 48$ into the equation $8x=48$. Dividing both sides by 8, we get $x=\frac{48}{8}=6$.

Answer:

The side - lengths are: three sides of length 6 meters and two sides of length $2.5\times6 = 15$ meters.