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Solve for x using the figure to the right.
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Solve For X Using The Figure To The Right X class=

Sagot :

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Answer:

x = 15

explanation:

we have to find both the hypotenuse of the triangles to solve this.

for the smaller triangle:

x² + 5² = h²

h = √x² + 5²

for the bigger triangle:

x² + 45² = h²

h = √x² + 45²

now that if you look, we found the sides - adjacent and leg side of the Δ

solving using Pythagoras theorem:

a² + b² = c²

(√x² + 45²)² + (√x² + 5²)² = 50²

x² + 2025 + x² + 25 = 2500

2x² = 450

x² = 225

x = ± 15

x = 15

Solution:

Finding the hypotenuse of the small triangle:

  • [tex]a^{2} = x^{2} + 5^{2}[/tex]
  • => [tex]\sqrt{a^{2}} = \sqrt{x^{2} + 5^{2}}[/tex]
  • => [tex]a = \sqrt{x^{2} + 25}[/tex]

Finding the hypotenuse of the big triangle:

  • [tex]b^{2} = x^{2} + 45[/tex]
  • [tex]\sqrt{b^{2} } = \sqrt{x^{2} + 45^{2} }[/tex]
  • [tex]b = \sqrt{x^{2} + 2025 }[/tex]

Finding the value of x.

  • [tex](45 + 5)^{2} = (\sqrt{x^{2} + 25} )^{2} + (\sqrt{x^{2} + 2025} )^{2}[/tex]
  • [tex](50)^{2} = (\sqrt{x^{2} + 25} )(\sqrt{x^{2} + 25} ) + (\sqrt{x^{2} + 2025} )(\sqrt{x^{2} + 2025} )[/tex]
  • [tex]2500 = x^{2} + 25 + {x^{2} + 2025}[/tex]
  • [tex]2500 = 2x^{2} + 2050[/tex]
  • [tex]450 = 2x^{2}[/tex]
  • [tex]225 = x^{2}[/tex]
  • [tex]x = \±15[/tex]
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