Question

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

Answer 1

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

Step-by-step 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.

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