Chapter 11, Problem 16SGR

To determine

Tofind:the distance of the home plate from the third base.

Answer to Problem 16SGR

  $65\sqrt{2}\text{ft}$ .

Explanation of Solution

Given:

The triangle formed by home plate, first base and second base is congruent to triangle formed by home plate, second base and third base.

Distance from the home plate to the first base is 65 feet. And the figure is shown below:

  

Calculation:

According to thequestion, the triangle formed by home plate, first base and second base is congruent to triangle formed by home plate, second base and third base.

  

Let x represent the distance between a catcher standing on the home plate and the short stop standing on the second base.

Therefore,

  $\begin{array}{l}{x}^2={65}^2+{65}^2\\ =4225+4225=8450\\ \therefore x=\sqrt{8450}=65\sqrt{2}\text{ft}\end{array}$ .

Hence, the distance of the home plate from the third baseis $65\sqrt{2}\text{ft}$ .