Answer:
[tex]d\approx 398\text{ m}[/tex]
Step-by-step explanation:
We can represent the length of the distance around the inside track with the equation:
[tex]d=2l + 2(\frac{1}2C)[/tex]
↓ substituting circumference of a circle formula: [tex]C = \pi d[/tex]
[tex]d = 2l + 2 \cdot \frac{1}2 \pi w[/tex]
↓ simplifying 2 · (1/2) = 1
[tex]d = 2l + \pi w[/tex]
where:
Plugging in the given values to solve for length, we get:
[tex]d = 2(100\text{ m}) + \pi(63\text{ m)}[/tex]
[tex]d = (200 + 63\pi)\text{ m}[/tex]
[tex]\boxed{d\approx 398\text{ m}}[/tex]
Further Note
The actual distance around the innermost lane of a standard running track is 400 meters. This divides nicely into common track and field event lengths, such as:
