Final answer:
To calculate the length of the diagonal walkway, use the Pythagorean theorem on the square garden with sides of 12 feet. The calculation is √(12² + 12²) = 12√2, which is approximately 17 feet. Therefore, the answer is B. 17 feet.
Step-by-step explanation:
Mr. Harrell is constructing a diagonal walkway through a square-shaped flower garden with each side measuring 12 feet. To find the length of the diagonal walkway, we can use the Pythagorean theorem, which applies to right triangles.
The theorem states that the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. In a square, the diagonal forms a right triangle with two of the sides of the square.
To calculate the diagonal, we use the formula c = √(a² + b²), where c is the diagonal, and a and b are the sides of the square. Since both a and b equal 12 feet, the formula becomes c = √(12² + 12²) = √(144 + 144) = √(288). We can simplify √(288) to 12√2, which is approximately 16.97 feet.
So, the length of the diagonal walkway is approximately 17 feet, which corresponds to option B.