Question

a rectangular dog park has a width that is 8 meters less than its length. if the perimeter is 54 feet, find the length, width, and area of the dog park.
input your answer in the provided text box below.

1. length
2. width
3. area

Explanation:

Step1: Define variables for length

Let length = $l$

Step2: Define width in terms of length

Width = $l - 8$

Step3: Use perimeter formula

Perimeter of rectangle: $P = 2(l + w)$
Substitute values: $54 = 2(l + (l - 8))$

Step4: Simplify and solve for $l$

$54 = 2(2l - 8)$
$27 = 2l - 8$
$2l = 27 + 8 = 35$
$l = \frac{35}{2} = 17.5$

Step5: Calculate width

Width = $17.5 - 8 = 9.5$

Step6: Calculate area

Area = $l \times w = 17.5 \times 9.5$

Answer:

1. Length: 17.5 meters
2. Width: 9.5 meters
3. Area: 166.25 square meters