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Mathematics, 06.10.2019 00:30 nathan123498

How does this model demonstrate the pythagorean theorem?

three squares whose corners touch so that the respective edges form a triangle. the smallest square has a side labeled six and is made up of thirty-six smaller squares. the largest square has a side labeled ten and is made up of one hundred smaller squares. the third square has a side labeled eight and is made up of sixty-four smaller squares.

a.
the sum of the lengths of the shortest and the longest sides is equal to twice the length of the middle side. so double the length of the longer leg of any right triangle is equal to the sum of the shorter leg and the hypotenuse.

b.
the sum of the area of the two smaller squares is equal to the area of the larger square. so the sum of the lengths of the two legs of any right triangle squared is equal to the length of the hypotenuse squared.

c.
the sum of the area of the smallest and the largest squares is equal to the area of the middle square. so the sum of the lengths of the shorter leg and the hypotenuse of any right triangle squared is equal to the length of the middle leg squared.

d.
the length of the longest side minus two equals the length of the middle side. the length of the middle side minus two equals the length of the shortest side. so the length of the short leg of any right triangle is equal to the length of the middle leg minus 2, and the length of the hypotenuse is equal to the length of the middle leg plus 2.

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How does this model demonstrate the pythagorean theorem?

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