Question

1. a rectangular portion of a park will be fenced off to create a playground. a construction company donated a total of 117.5 feet of fencing. based on the space provided to create the playground, the length of the playground must be 35.5 feet. use the formula for the perimeter of a rectangle to determine what the width of the playground must be.

Explanation:

Step1: Recall perimeter formula

The perimeter formula for a rectangle is $P = 2l+2w$, where $P$ is the perimeter, $l$ is the length and $w$ is the width. We know $P = 117.5$ feet and $l=35.5$ feet.

Step2: Substitute values into formula

Substitute the known values into the formula: $117.5 = 2\times35.5+2w$.

Step3: Simplify the right - hand side

First, calculate $2\times35.5 = 71$. So the equation becomes $117.5=71 + 2w$.

Step4: Isolate the term with $w$

Subtract 71 from both sides of the equation: $117.5−71=2w$. So, $46.5 = 2w$.

Step5: Solve for $w$

Divide both sides by 2: $w=\frac{46.5}{2}=23.25$ feet.

Answer:

23.25 feet