Question

This question will have a picture attached. Noah ran around the track two times. How far did he run in feet? Round your answer to the nearest whole number. (That measurement showing in the bottom of the photo is 20ft and the one showing on the side is 10 ft if they are cut off or difficult to see. )

Answer 1

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

Let's find the perimeter:

Bottom = 10 ft

Top = 10 ft

Right =

`C_{\text{half}}=(\pi d)/(2)=(\pi(10))/(2)=5\pi`

Left =

`C_{\text{half}}=(\pi d)/(2)=(\pi(10))/(2)=5\pi`

Thus, the perimeter is

`\begin{gathered} P=10+10+5\pi+5\pi \\ P=20+10\pi \end{gathered}`

Let's multiply this by 2, so we get:

`\begin{gathered} 2*(20+10\pi) \\ =40+20\pi \end{gathered}`

Using a calculator, we find the answer:

`40+20\pi\approx102.83`

Rounded to the nearest whole number,

`103ft`

Answer103 ft