Question

4. The official distance between home plate and second base in a baseball diamond is 122 feet. Find the area of the official ball diamond and the distances between the bases. (The official ball diamond is in the form of a square ) 5. A rectangular flower garden is to be enclosed by a fence. Its dimensions are 27.15 ft. by 32.75 ft. How many meters of fencing are needed? How many square meters does the garden contain ? (1 meter = 3.28 ft.)

Answer 1

The official baseball diamond's side length is about 86.36 feet and its area is about 7461.56 square feet. As for the enclosed rectangular garden, it requires about 36.53 meters of fencing and its area is approximately 82.65 square meters.

Step-by-step explanation:

The official baseball diamond is in the shape of a square. Given that the distance from home plate to second base is 122 feet, this implies that the diagonal of the square is 122ft. In a square, the diagonal equals the side length multiplied by the square root of 2. By rearranging, we can calculate the side length as the diagonal divided by the square root of 2, which equals to about 86.36 feet. The area of the square field is then calculated as side length squared, which is about 7461.56 square feet.

For the second part of the question, a rectangular flower garden is to be enclosed by a fence. The amount of fencing needed is equal to the perimeter of the rectangle, which is 2 times the sum of the length and width. Converting the feet to meters (by dividing the values by 3.28), we get the length as about 8.27 meters and the width as about 9.99 meters. The total amount of fencing needed is about 36.53 meters. The distance area of the garden in square meters can be found by multiplying length by width, giving approximately 82.65 square meters.

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