Question

A particular baseball diamond is actually a square with 7575​-foot sides. What is the distance from home plate to second​ base? Express the answer in simplified radical form. Then find a decimal approximation.

Answer 1

`75√(2)\approx 106.07` feet.

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:

`x^2=75^2+75^2`

`x^2=2(75^2)`

Now, we will take positive square root of both sides as:

`√(x^2)=√(2(75^2))`

`x=75√(2)`

`x=106.066017\approx 106.07`

Therefore, the exact distance from home plate to second​ base is
`75√(2)` feet or approximately 106.07 feet.