Question

A major baseball diamond is a square with side lengths of 90 feet.

a) What is the distance from home plate to second base (Going directly from home base to 2nd base, so draw a line that goes from home base staright to 2nd base).

b) Suppose you want to position the pitching mound at equal distances between 2nd base and home plate, how far from the homeplate should you place the pitching mound.

*It is helpful to draw a picture to get a good visual

Blank 1:
Blank 2:

Answer 1

Answer:
`\bold{a)\quad 90\sqrt2\qquad \qquad b)\quad 45\sqrt2}`

Explanation:

Since you are looking for the distance from home plate to second base, you are actually looking for the length of the diagonal of the square. Use the Pythagorean Theorem: a² + b² = c² where a and b are the side lengths and c is the length of the diagonal.

`90^2+90^2=c^2\\8100+8100=c^2\\16200=c^2\\√(16200)=c\\\boxed{90\sqrt2}=c\qquad \qquad \text{which is approximately 127.28}\\\\\\\\\text{Halfway between home plate and 2nd base means divide that length by 2:}\\\\(90\sqrt2)/(2)=\boxed{45\sqrt2}`