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mariarad [96]
2 years ago
11

If you think you know the answers to this please let me know because I’ve been stuck on this for so long

Mathematics
1 answer:
alexira [117]2 years ago
5 0

The equations that express the relationship between the side lengths of the triangles are

  • 10² = 6² + 8²
  • (\sqrt{8} )^{2}  = (\sqrt{5} )^{2} + (\sqrt{3} )^{2}
  • (\sqrt{30} )^{2} = 5^{2} + (\sqrt{5} )^{2}
  • (\sqrt{37} )^{2}  = 1^{2} + 6^{2}
  • 3^{2} = (\sqrt{2} )^{2} + (\sqrt{7} )^{2}

<h3>Pythagorean triple</h3>

From the question, we are to write an equation that expresses the relationship between the side lengths of each triangle

From the Pythagorean theorem,

In a right triangle, the square of the longest side (hypotenuse) equals sum of squares of the other two sides

That is,

c² = a² + b²

Where c is the longest side (hypotenuse)

a and b are the other two sides

  • For 10, 6, 8

The equation is

10² = 6² + 8²

  • For \sqrt{5}, \sqrt{3}, \sqrt{8}

The equation is

(\sqrt{8} )^{2}  = (\sqrt{5} )^{2} + (\sqrt{3} )^{2}

  • For 5, \sqrt{5}, \sqrt{30}

The equation is

(\sqrt{30} )^{2} = 5^{2} + (\sqrt{5} )^{2}

  • For 1, \sqrt{37}, 6

The equation is

(\sqrt{37} )^{2}  = 1^{2} + 6^{2}

  • For 3, \sqrt{2}, \sqrt{7}

The equation is

3^{2} = (\sqrt{2} )^{2} + (\sqrt{7} )^{2}

Hence, the equations that express the relationship between the side lengths of the triangles are

  • 10² = 6² + 8²
  • (\sqrt{8} )^{2}  = (\sqrt{5} )^{2} + (\sqrt{3} )^{2}
  • (\sqrt{30} )^{2} = 5^{2} + (\sqrt{5} )^{2}
  • (\sqrt{37} )^{2}  = 1^{2} + 6^{2}
  • 3^{2} = (\sqrt{2} )^{2} + (\sqrt{7} )^{2}

Learn more on Pythagorean triple here: brainly.com/question/3223211

#SPJ1

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