a rectangular dog park has a width that is 8 meters less than its length. if the perimeter is 54 feet, find…

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.\ninput your answer in the provided text box below.\n1) length\n2) width\n3) area

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.\ninput your answer in the provided text box below.\n1) length\n2) width\n3) area

Answer

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