nsavility nsavility
  • 22-07-2020
  • Mathematics
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Find the value of x. Please help! Thanks.

Find the value of x Please help Thanks class=

Respuesta :

gmany
gmany gmany
  • 23-07-2020

Answer:

[tex]\huge\boxed{x=\sqrt{30}}[/tex]

Step-by-step explanation:

ΔABC and ΔBDC are similar (AAA).

Therefore the corresponding sides are in proportion:

[tex]\dfrac{AC}{BC}=\dfrac{BC}{CD}[/tex]

substitute

[tex]AC=7+3=10\\{BC}=x\\CD=3[/tex]

[tex]\dfrac{10}{x}=\dfrac{x}{3}[/tex]           cross multiply

[tex](10)(3)=(x)(x)\\\\30=x^2\\\\x^2=30\to x=\sqrt{30}[/tex]

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