The problem in your image involves calculating the distance from home plate to second base on a baseball diamond, which is shaped as a square. The distance between each base (side of the square) is given as 90 feet, and the task is to find the diagonal distance from home plate to second base.

This forms a right triangle, where:

• The two legs of the triangle are each 90 feet (the distances from home to first and first to second).
• The diagonal (hypotenuse) is the distance from home plate to second base.

Using the Pythagorean theorem: $d^2 = 90^2 + 90^2$ $d^2 = 8100 + 8100 = 16200$ $d = \sqrt{16200} = 90\sqrt{2}$

Thus, the distance from home plate to second base is $90\sqrt{2}$ feet, which matches option A.

Would you like more details or have any questions?

Here are 5 related questions:

1. How do we apply the Pythagorean theorem in real-world scenarios?
2. Why is the distance from home plate to second base a diagonal?
3. How would the result change if the distance between bases was different?
4. What other shapes can be analyzed using the Pythagorean theorem?
5. How does the square root of 2 appear in other geometric problems?

Tip: Whenever you encounter problems involving squares or rectangles, think about diagonals and the Pythagorean theorem to simplify calculations.