alemankatya28
alemankatya28 alemankatya28
  • 02-04-2020
  • Mathematics
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What’s the answer to this?

Whats the answer to this class=

Respuesta :

nktselepov
nktselepov nktselepov
  • 02-04-2020

Since the triangle is equilateral, all its angles are equal to 60°

AO is the bisector⇒∠OAD = 30°

AO is the hypotenuse, ∠OAD = 30°⇒

OD=5*2=10m

By the Pythagorean theorem

[tex]10^2=AD^2+5^2\\AD=\sqrt{100-25} \\AD=\sqrt{75}[/tex]

[tex]AC=AD+DC=2\sqrt{75}=10\sqrt{3}[/tex]

[tex]S=\frac{a^2\sqrt{3} }{4}[/tex]

[tex]S=\frac{(10\sqrt{3})^2\sqrt{3} }{4} =\frac{300\sqrt{3} }{4} =75\sqrt{3} m^2[/tex]

Answer: A) [tex]S=75\sqrt{3}[/tex]m²

P.S. Hello from Russia and sorry for my bad english :^)

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