Question

The layout of a Little League playing field is a square 60 feet on a side. How far is it directly from home plate to second base (the diagonal of the square)?

Short answer

The distance from home plate to second base is approximately 84.84 feet.

Step-by-step solution

Understand the Problem

The problem states that a Little League playing field is a square with sides of 60 feet each. We need to find the distance from home plate to second base, which is along the diagonal of the square.

Identify Key Formula

To find the diagonal of a square, use the formula for the diagonal of a square where side length is given by: \[ d = s \times \sqrt{2} \] where \( s \) is the side length.

Plug in the Given Values

Here, \( s = 60 \) feet. Using the formula for the diagonal, substitute 60 for \( s \): \[ d = 60 \times \sqrt{2} \]

Calculate the Diagonal

Evaluate the expression: \[ d = 60 \times 1.414 = 84.84 \] Therefore, the diagonal (distance from home plate to second base) is approximately 84.84 feet.

Key concepts

Diagonal of a Square

This calculation gives us approximately 84.84 feet, which is the distance from home plate to second base.

Distance Calculation

This matches our earlier calculation using the square's diagonal formula. Whether using the shortcut formula or Pythagorean Theorem, you get the same answer, confirming your understanding.

Square Geometry

Squares are fascinating shapes with some helpful properties. A square has four equal sides and four right-angled corners. When you draw a line from one corner to the opposite (the diagonal), you split the square into two identical right-angled triangles.
Each side of a square gives you a lot of information. For instance, the area of a square can be calculated by squaring the side length ( s^2 ). Knowing the properties of these shapes makes solving related problems much easier.
In models like the Little League field, recognizing that it's a square helps. You can use properties like equal side lengths and the Pythagorean Theorem to solve for the diagonal. Understanding square geometry ensures you can apply this knowledge not only in textbooks but also in real-life situations.