A baseball diamond is a square that is 90′ on each side. If a player throws the ball from 2nd base to home, how far will the ball travel?

So we are given that each side of a square is 90 feet.
By finding how far the ball will travel, we are basically finding the distance from 2nd base to home
Well, let’s picture a baseball field, and we find out that they are diagonally across from one another.
Well, let’s draw a diagonal connecting home to 2nd base.
Since the field is a square, it has a right angle at 1st base
We now know 2 legs in a right triangle, that calls for the
(You could also do 45-45-90 special right triangle, which would give you the answer very quickly)
So we have ##90^2 + 90^2 = c^2##
Which is ##16200 = c^2##
We are finding ##c##, so ##sqrt(16200) = c##
We can simplify this to ##sqrt(162*100)## which is ##10sqrt(162)##
Then we can simplify this to ##10sqrt(81*2)##, which is ##10*9sqrt(2)##
Finally, we multiply the values outside of the root to get our final answer ##90sqrt2##
And we are done.