The diagram shows the back fences of three houses in a small neighborhood. The lengths of the fences are given.

Pythagorean theorem: a2 + b2 = c2

Triangles

Use the Pythagorean theorem to classify the triangle formed by the three fences. Which is true about the numbers 5, 12, and 13?
They are a Pythagorean triple that does not form a right triangle.
They are a Pythagorean triple that forms a right triangle.
They do not satisfy the Pythagorean theorem, but they do form a right triangle.
They do not satisfy the Pythagorean theorem, and they do not form a right triangle.

For the length of the fences given (5, 12 and 13 units), the true fact from the specified options is given by: Option B: They are a Pythagorean triple that forms a right triangle.

What is Pythagoras Theorem?

If ABC is a triangle with AC as the hypotenuse and angle B with 90 degrees then we have:

[tex]|AC|^2 = |AB|^2 + |BC|^2[/tex]

where |AB| = length of line segment AB. (AB and BC are rest of the two sides of that triangle ABC, AC being the hypotenuse).

What are pythagorean triple?

3 positive integers such that they satisfy pythagorean theorem are called pythagorean triples.

For any pythagorean triple, a corresponding right angled triangle can be constructed with its lengths same as those 3 integers in that triple.

For this case, the given values are 5,12 and 13

If it forms a right angled triangle, then as in a right angled triangle, the longest side is hypotenuse, so 13 is hypotenuse (by assumption that 5,12, and 13 can form a right angled triangle).

The other two sides would be of 12 and 5 units.

Thus, if they are pythagorean triple, they should satisfy the pythagoras theorem.

[tex]13^2 = 169,\\\\12^2 + 5^2 = 144 + 25 = 169\\[/tex]

Thus, we get:

[tex]13^2 = 12^2 + 5^2[/tex]

Thus, 5,12 and 13 are pythagorean triple, and therefore, they can form a right angled triangle.

Thus, for the length of the fences given (5, 12 and 13 units), the true fact from the specified options is given by: Option B: They are a Pythagorean triple that forms a right triangle.

Learn more about Pythagoras theorem here:

https://brainly.com/question/12105522

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