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On a baseball diamond,1st base, 2nd base, 3rd base, and home plate form a square. If the ball is thrown from 1st base to 2nd base and then from 2nd base to home plate, how many feet has the ball been thrown? The distance between the bases are 90 feet. Option A: 90 Sq. root of 2 Option B: 180 Sq. Root of 2 Option C: 90+90 Sq. Root of 2 Option D: 270 Sq. Root of 2

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Answer:

Option C: 90+90 Sq. Root of 2

Step-by-step explanation:

First we find the distance from second base to home plate.  This is the diagonal of the square, which splits it into two right triangles.

Each right triangle will have legs of 90 feet.  We use the  Pythagorean theorem to find the length of the diagonal (the hypotenuse of the right triangle):

a² + b² = c²

90² + 90² = c²

8100 + 8100 = c²

16200 = c²

Take the square root of each side:

√(16200) = √(c²)

Simplifying √16200, we find the prime factorization:

16200 = 162(100)

162 = 2(81)

81 = 9(9) [Since this is a perfect square, we can stop; we know we take this out of the radical.]

100 = 10(10) [Since this is a perfect square, we can stop; we know we take this out of the radical.]

√16200 = √(9²×10²×2) = 9×10√2 = 90√2

This means the distance from 1st to 2nd and then from 2nd to home would be

90 + 90√2

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