Question: 3. a) Steve is turning half of his backyard into a chicken pen. His backyard is a rectangle that…

3. a) Steve is turning half of his backyard into a chicken pen. His backyard is a rectangle that measures 20.6 meters by 45 meters. He wants to put a chicken wire fence that stretches diagonally from one corner to the opposite corner. How much wire fencing will he need?

[Diagram of a rectangle with a diagonal line from one corner to the opposite corner. The dimensions are 45 m and 20.6 m.]

Solution

To find the length of wire fencing needed, we can calculate the diagonal of the rectangle using the Pythagorean theorem. The rectangle has a width of 20.6 meters and a height of 45 meters. Apply the Pythagorean theorem: \[ c = \sqrt{a^2 + b^2} \] where: - \( c \) is the diagonal, - \( a = 20.6 \) meters, - \( b = 45 \) meters. First, square the width and height: \[ a^2 = 20.6^2 = 424.36 \] \[ b^2 = 45^2 = 2025 \] Add the squares of the width and height: \[ a^2 + b^2 = 424.36 + 2025 = 2449.36 \] Take the square root to find the length of the diagonal: \[ c = \sqrt{2449.36} \approx 49.49 \] Therefore, Steve will need approximately 49.49 meters of wire fencing.