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A baseball diamond is a square with a side length of 90 ft. What is the distance from first base to third base in simplest radical form?

Sagot :

Answer:

90[tex]\sqrt{2}[/tex] ft.

Step-by-step explanation:

Using the Pythagorean theorem we get 90^2 + 90^2 = d^2 where d is the distance from 1st base to third base.  So, d^2 = 8100 + 8100 = 16200

d = [tex]\sqrt{16200}[/tex] = 90[tex]\sqrt{2}[/tex].   An easier way to do this is to recognize that the triangle formed by the diagonal of the baseball diamond and the two base paths from home to first and third is a 45-45-90 triangle.  Therefore, the hypontenuse (diagonal) equals [tex]\sqrt{2}[/tex] times a leg (90 ft.)

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