## Real World Applications – Algebra I

### Topic

Baseball Diamonds

### Student Exploration

One of the most popular uses of taking square roots is finding the dimensions of a square given the area. We are going to apply our knowledge of taking square roots and irrational numbers to different baseball diamonds and compare the differences between little league and professional diamonds.

Most people know that the dimensions of a regulation-sized baseball diamond are 90ft by 90ft. This means that the area is 8100 square feet because \begin{align*}90 \times 90 = 8100\end{align*}, or the square root of 8100 is 90. If we were to work backwards and say that we had 80 square feet for a baseball diamond, we could take the square root of 8100 to find the dimensions.

For a little league baseball diamond, the dimensions are a little different. The area of a little league diamond is 3600 square feet. What are the dimensions?

The dimensions are 60ft by 60ft, because \begin{align*}60 \times 60 = 3600\end{align*}, or the square root of 3600 is 60.

### Extension Investigation

We can also compare the little league and professional baseball diamonds in comparison of their area. We can find out how much smaller the little league diamond is, or what percent smaller it is in comparison to the professional size.

We can divide the area of the little league diamond by the professional diamond and multiply by 100 to find out how much smaller the little league diamond is.

\begin{align*}\frac{3600}{8100} &= 0.44\\ 0.44 \times 100 &= 44\%\end{align*}

Little league diamonds are 44% the area of professional baseball diamonds.

What about softball diamonds? Look up to see if they’re similar or different from baseball diamonds. Why do you think they’re similar or different?