Question

A baseball diamond is a square 90 feet on each side. Suppose the pitcher is in the exact middle of the diamond and the batter hits a ball to the first baseman. The pitcher needs to run to first base (to receive the throw from the first baseman) before the batter can get there. How much shorter is the pitcher's run to the base than the batter's?

Answer 1

@perl @igreen I need help!

Answer 2

Thanks for coming :D

Answer 3

Hello? Are you here? Most people just said 45, but I thought it would have been more complicated

Answer 4

you can use pythagorean theorem

Answer 5

90^2+90^2= h^2?

Answer 6

I mean c^2

Answer 7

90 is the hypotenuse here

Answer 8

\[\sqrt90^2+90^2=c\]

Answer 9

so 90/2?

Answer 10

$$
\Large{
x^2 + x^2 = 90^2
\\ 2x^2 = 90^2 \\~\\
\\ x^2 = \frac{90^2}{2} \\~\\
\\ x = \sqrt{\frac{90^2}{2}}
\\~\\
\\ x = \frac{\sqrt{90^2}}{\sqrt2 } \\~\\
\\ x = \frac{90}{\sqrt2 }
}
$$

Answer 11

You can't get the square root of 2...

Answer 12

you can rationalize the denominator

Answer 13

$$
\Large{
x^2 + x^2 = 90^2
\\ 2x^2 = 90^2 \\~\\
\\ x^2 = \frac{90^2}{2} \\~\\
\\ x = \sqrt{\frac{90^2}{2}}
\\~\\
\\ x = \frac{\sqrt{90^2}}{\sqrt2 }
\\~\\ x = \frac{90}{\sqrt2 }
\\~\\ x = \frac{90}{\sqrt2 }\cdot \color{red}{\frac{\sqrt2 }{\sqrt2}}

\\~\\ x = \frac{90 \cdot \sqrt2 }{2}

\\~\\ x = \color{blue}{45\cdot \sqrt 2 }
}
$$

Answer 14

so 45 was it?

Answer 15

45 times square root 2

Answer 16

which is about 63.6396 in decimal

Answer 17

ok, thanks :D

Answer 18

but the question asks, how much shorter

Answer 19

$$ \Large 90 - 45 \sqrt 2$$

Answer 20

=27ish?