Question

a baseball diamond is a square with sides of 90 feet. What is the shortest distance, to the nearest tenth of a foot, between first and third base?

Answer 1

To find the shortest distance between first and third base on a baseball diamond with sides of 90 feet, we use the Pythagorean theorem. The diagonal of a square (the distance between first and third base) is the side length times the square root of 2. This gives a distance of approximately 127.3 feet.

Step-by-step explanation:

The question "a baseball diamond is a square with sides of 90 feet. What is the shortest distance, to the nearest tenth of a foot, between first and third base?" involves using the Pythagorean theorem to find the diagonal of a square, which represents the distance between first and third base in a baseball diamond. Since a baseball diamond is in the shape of a square, the two bases are opposite corners of the square. The formula for the diagonal (D) of a square with side length (s) is D = s√2, since the diagonal forms a right triangle with the sides of the square.

To calculate the distance:

1. Substitute the side length of 90 feet into the formula: D = 90√2.
2. Calculate the diagonal: D = 90√2 = 90 * 1.414 (approximately).
3. Find the result: D ≈ 127.3 feet to the nearest tenth of a foot.

Therefore, the shortest distance between first and third base on a baseball diamond is 127.3 feet to the nearest tenth of a foot.

Answer 2

127.3 feet This problem requires the use of pythagoras theorem. Ignore the face that it's a baseball diamond. All you're concerned with is that you have a square that's 90 feet per side and you want to know what the length of the diagonal. So you have a right triangle with 2 sides of 90 feet each and you want to know the length of the hypotenuse. The formula is C^2 = A^2 + B^2 Both A and B are 90, so plugging them into the formula gives C^2 = 90^2 + 90^2 = 8100 + 8100 = 16200 So C^2 = 16200 Take the square root of both sides C = 127.2792 Round to the nearest tenth, giving C = 127.3