A baseball diamond is a square with sides of 90 feet. What is the shortest distance between first base and third base?
Draw a picture:
Solve:
To find the shortest distance between first base and third base, we can use the Pythagorean theorem.
Let's consider the diagonal of the square (from first base to third base) as the hypotenuse of a right triangle with sides of 90 feet each.
Using the Pythagorean theorem, we have:
\(a^{2} + b^{2} = c^{2}\)
\(90^{2} + 90^{2} = c^{2}\)
\(8100 + 8100 = c^{2}\)
\(16200 = c^{2}\)
Taking the square root of both sides, we get:
\(c = \sqrt{16200}\)
\(c ≈ 127.28 \text{ feet}\)
Therefore, the shortest distance between first base and third base is approximately 127.28 feet.