Question

Tara is shown a picture of a dart board along with some dimensions. She knows that each triangular section in the dartboard is congruent. What is the approximate length of arc x?

Answer 1

The approximated length of arc x is 4 inches ⇒ C

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