Question: The image shows a rectangle with a diagonal line drawn from one corner to the opposite corner. The…

The image shows a rectangle with a diagonal line drawn from one corner to the opposite corner. The dimensions of the rectangle are labeled as 45 m and 20.6 m. There are handwritten notes on the right side of the image, including the Pythagorean theorem \( c^2 = a^2 + b^2 \), where \( a = 20.6 \) m and \( b = 45 \) m. The notes also mention that \( c \) is the diagonal.

The question at the bottom of the image asks: b) What is the perimeter of the chicken pen? What is the area?

Solution

To find the perimeter and area of the chicken pen, we’ll treat it as a rectangle with the given dimensions of 45 meters and 20.6 meters. First, calculate the perimeter. The formula for the perimeter \(P\) of a rectangle is: \[ P = 2l + 2w \] where \(l\) is the length and \(w\) is the width. Substitute the given values: \(l = 45\) m and \(w = 20.6\) m \[ P = 2(45) + 2(20.6) \] \[ P = 90 + 41.2 \] \[ P = 131.2 \text{ m} \] Now, calculate the area. The formula for the area \(A\) of a rectangle is: \[ A = lw \] Substitute the given values: \[ A = 45 \times 20.6 \] \[ A = 927 \text{ m}^2 \] Therefore, the perimeter of the chicken pen is 131.2 meters, and the area is 927 square meters.