Answer:
[tex]75\sqrt{2}\approx 106.07[/tex] feet.
Step-by-step explanation:
Please find the attachment.
We have been that a particular baseball diamond is actually a square with 75-foot sides.
We can see that distance from home plate to second base would be equal to hypotenuse with each leg of 75-ft.
We will use Pythagoras theorem to find the distance x as:
[tex]x^2=75^2+75^2[/tex]
[tex]x^2=2(75^2)[/tex]
Now, we will take positive square root of both sides as:
[tex]\sqrt{x^2}=\sqrt{2(75^2)}[/tex]
[tex]x=75\sqrt{2}[/tex]
[tex]x=106.066017\approx 106.07[/tex]
Therefore, the exact distance from home plate to second base is [tex]75\sqrt{2}[/tex] feet or approximately 106.07 feet.
