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MAXImum [283]
3 years ago
15

Use a calculator to find the missing side length. Tell whether the side lengths form a Pythagorean Triple.

Mathematics
1 answer:
12345 [234]3 years ago
5 0
Pythagorean theorem: a^2 + b^2 = c^2
The hypotenuse is always the c in the equation.  
If the two side lengths they gave you are not the hypotenuse, then enter
4.5^2 + 5.6^2 in the calculator, then find the square root of that. :-)
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If the area of a baseball diamond (shape of a square) is 8100 ft squared, how would you find the distance from 1st base to 3rd b
Readme [11.4K]

Answer:

  • Exact distance = 90\sqrt{2} feet
  • Approximate distance = 127.2792 feet.

===========================================================

Explanation:

The area of the square is 8100 square feet, abbreviated ft^2.

Apply the square root to find the distance from any base to its adjacent counterpart (eg: from 1st to 2nd base). So we get sqrt(8100) = 90 ft as that side distance. Notice that 90*90 = 8100.

If you were to draw a line from 1st base to 3rd base, then you would split the square into two congruent right triangles. Each right triangle is isosceles (the two legs being 90 ft each).

Use the pythagorean theorem to find the hypotenuse.

a^2 + b^2 = c^2\\\\c = \sqrt{a^2+b^2}\\\\c = \sqrt{90^2+90^2}\\\\c = \sqrt{2*90^2}\\\\c = \sqrt{2}*\sqrt{90^2}\\\\c = \sqrt{2}*90\\\\c = 90\sqrt{2} \ \text{ ... exact distance}\\\\c \approx 127.2792 \ \text{ ... approximate distance}\\\\

The distance from 1st to 3rd base is roughly 127.2792 feet.

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