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.
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1. length
2. width
3. area

Explanation:

Step1: Define variables for length

Let length = $l$ meters

Step2: Express width in terms of length

Width = $l - 8$ meters

Step3: Use perimeter formula for rectangle

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

Step4: Simplify and solve for $l$

$2(2l - 8) = 54$
$4l - 16 = 54$
$4l = 54 + 16 = 70$
$l = \frac{70}{4} = 17.5$

Step5: Calculate width

$w = 17.5 - 8 = 9.5$ meters

Step6: Calculate area of rectangle

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

Answer:

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