Question

A baseball infield is a square, each side measuring 90 feet. To the nearest foot, what is the distance from home plate to second base?

Answer 1

Using the Pythagorean theorem, the distance from home plate to second base, which is the diagonal of a square with 90-foot sides, is approximately 127 feet to the nearest foot.

Step-by-step explanation:

The distance from home plate to second base on a baseball infield, which is a square with each side measuring 90 feet, can be found using the Pythagorean theorem. We calculate the distance as the diagonal of the square, which is the hypotenuse of a right triangle whose legs are the sides of the square.

According to the Pythagorean theorem, the formula to calculate the hypotenuse (c) is:

c = √(a^2 + b^2)

Here, both sides a and b equal 90 feet. Substituting the values, we get:

c = √(90^2 + 90^2)

Which simplifies to:

c = √(8100 + 8100)

c = √(16200)

c ≈ 127 feet

To the nearest foot, it's approximately 127 feet from home plate to second base.

Answer 2

Using the Pythagorean theorem:

90^2 +90^2 = X^2

8100 + 8100 = x^2

16,200 = x^2

X = √16,200

X = 127.28 feet.

Rounded to the nearest foot = 127 feet.