The track consists of two straight lines (top and bottom) and two curve lines (right and left).
We will find the perimeter of the figure and multiply it by '2' since Noah ran around the track two times.
We know the curved region is half of a circle. So, we will find the length of this curved part by using the circumference of half circle formula.
Note: the Diameter (d) of the circle is 10 ft
Bottom = 10 ft
Top = 10 ft
Right =
[tex]C_{\text{half}}=\frac{\pi d}{2}=\frac{\pi(10)}{2}=5\pi[/tex]Left =
[tex]C_{\text{half}}=\frac{\pi d}{2}=\frac{\pi(10)}{2}=5\pi[/tex]Thus, the perimeter is
[tex]\begin{gathered} P=10+10+5\pi+5\pi \\ P=20+10\pi \end{gathered}[/tex]Let's multiply this by 2, so we get:
[tex]\begin{gathered} 2\times(20+10\pi) \\ =40+20\pi \end{gathered}[/tex]Using a calculator, we find the answer:
[tex]40+20\pi\approx102.83[/tex]Rounded to the nearest whole number,
[tex]103ft[/tex]Answer103 ft