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german
2 years ago
14

Tara is shown a picture of a dart board along with some dimensions. She knows that each triangular section in the dartboard is c

ongruent. What is the approximate length of arc x?

Mathematics
1 answer:
Romashka [77]2 years ago
4 0

Answer:

The approximated length of arc x is 4 inches ⇒ C

Step-by-step explanation:

  • The diameter of the outer circle is 28 inches
  • There is a boundary with width 2 inches

That means the diameter of the inner circle is less than the diameter of the outer circle by 4 inches (2 in from each side)

  • The diameter of the inner circle = 28 - 4 = 24 inches

The circumference of the inner circles formed from 20 congruent arcs of length x inches

  • The circumference of the inner circle = 20 x

Now let us find x

The formula of the circumference of a circle is C = π d, where d is the diameter of the circle

∵ The diameter of the inner circle is 24 inches

∴ d = 24

∴ C = 24 π

∵ C = 20 x

- Equate 20 x by 24 π

∴ 20 x = 24 π

- Divide both sides by 20

∴ x = 3.769911184

- Round it to the nearest unit

∴ x ≅ 4

The approximated length of arc x is 4 inches

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