Question

a major league baseball \diamond\ is actually a square, 90 feet on a side (see the figure). what is the distance directly from first base to third base (the diagonal of the square)? the distance directly from first base to third base is approximately □ feet. (type an integer or decimal rounded to two decimal places as needed.)

Explanation:

Step1: Apply Pythagorean theorem

In a square, if the side - length is $a = 90$ feet, and the diagonal $d$ is the hypotenuse of a right - triangle formed by two adjacent sides. According to the Pythagorean theorem $d^{2}=a^{2}+a^{2}$.

Step2: Substitute the value of $a$

Since $a = 90$, then $d^{2}=90^{2}+90^{2}=8100 + 8100=16200$.

Step3: Solve for $d$

$d=\sqrt{16200}=90\sqrt{2}\approx90\times1.414214 = 127.28$ feet.

Answer:

$127.28$