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What is the value of X in the figure below? In this diagram ∆ABD is similar to ∆CAD.

What is the value of X in the figure below In this diagram ABD is similar to CAD class=

Respuesta :

mhanifa

Answer:

  • F. 45/4

Step-by-step explanation:

Corresponding sides have same ratio:

  • AB/AC = BD/AD

Find AB:

  • AB = [tex]\sqrt{20^2-15^2} = 5\sqrt{7}[/tex]

Find AD:

  • AD = √15²-x²

Now the ratio:

  • 5√7/15 = (20 - x)/√(15²-x²)
  • √7 *√(225-x²)= 3(20 - x)
  • 7(225 - x²) = 9(20 -x)²
  • 7*225 - 7x² = 9(400 - 40x + x²)
  • 1575 - 7x² = 3600 - 360x + 9x²
  • 16x² - 360x + 2025 = 0
  • (4x)² - 2*4x*45 + 45² = 0
  • (4x - 45)² = 0
  • 4x - 45 = 0
  • 4x = 45
  • x = 45/4

Correct choice is F

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