Question

We know that a triangle with side lengths , , and is a right triangle. Using those side lengths, find the missing triples and x-values. Write the triples in parentheses, without spaces between the numbers, and with a comma between numbers. Write the triples in order from least to greatest. Type the correct answer in each box.

Answer 1

The completed table for the Pythagorean triples are:

$x \text{ value } \text{ Pythagorean triple}\\\text{ } \text{ } \text{ } 3 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (6,8,10)\\\text{ } \text{ } \text{ } 4 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (8,15,17)$

  $\text{ } \text{ } \text{ } 5 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (10,24,26)\\\text{ } \text{ } \text{ } 6 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (12,35,37)$.

A trio of positive numbers known as a Pythagorean triple fits into the Pythagoras theorem's formula, which is written as a² + b² = c², where a, b, and c are all positive integers. Here, "a" and "b" make up the other two legs of the right-angled triangle, and "c" serves as the triangle's "hypotenuse," or longest side. In terms of the Pythagorean triples (a, b, c).

In the question, we are given that a triangle with side lengths x² - 1, 2x, x² + 1 is a right triangle, and are asked to fill in the missing table:

$x \text{ value } \text{ Pythagorean triple}\\\text{ } \text{ } \text{ } 3 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \underline{\text{ }}\\\text{ } \text{ } \text{ } \underline{\text{ }} \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (8,15,17)$

  $\text{ } \text{ } \text{ } 5 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \underline{\text{ }}\\\text{ } \text{ } \text{ } \underline{\text{ }} \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (12,35,37)$.

Taking x as 3, and putting in the sides, we get:

x² + 1 = 3² + 1 = 10.

2x = 2*3 = 6.

x² - 1 = 3² - 1 = 8.

Thus, the triplet is 6,8,10.

For the triplet 8,15,17, we get the x value as:

2x = 8,

or, x = 8/2 = 4.

Thus, the x-value for the triplet (8,15,17) is 4.

Taking x as 5, and putting in the sides, we get:

x² + 1 = 5² + 1 = 26.

2x = 2*5 = 10.

x² - 1 = 5² - 1 = 24.

Thus, the triplet is 10,24,26.

For the triplet 12,35,37, we get the x value as:

2x = 12,

or, x = 12/2 = 6.

Thus, the x-value for the triplet (12,35,37) is 6.

Thus, the completed table for the Pythagorean triples are:

$x \text{ value } \text{ Pythagorean triple}\\\text{ } \text{ } \text{ } 3 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (6,8,10)\\\text{ } \text{ } \text{ } 4 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (8,15,17)$

  $\text{ } \text{ } \text{ } 5 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (10,24,26)\\\text{ } \text{ } \text{ } 6 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (12,35,37)$.

Learn more about the Pythagorean triplets at

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The provided question is incomplete. The complete question is:

"We know that a triangle with side lengths x² - 1,2x and x² + 1 is a right triangle. Using those side lengths, find the missing triples and x-values.

Write the triples in parentheses, without spaces between the numbers, and with a comma between numbers. Write the triples in order from least to greatest.

Type the correct answer in each box.

$x \text{ value } \text{ Pythagorean triple}\\\text{ } \text{ } \text{ } 3 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \underline{\text{ }}\\\text{ } \text{ } \text{ } \underline{\text{ }} \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (8,15,17)$

  $\text{ } \text{ } \text{ } 5 \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \underline{\text{ }}\\\text{ } \text{ } \text{ } \underline{\text{ }} \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } \text{ } (12,35,37)$.