Question

Your Assignment

Injured runners train on a special track at a rehabilitation center. The track is a square with a half circle on its left and right sides. The area of the square is 128 square feet. What is the length of the track? Use the table to help you answer the questions.

Square 11.02 11.12 11.22 11.32 11.42 11.52
Value 121.0 123.2 125.4 127.7 130.0 132.3
Square 11.62 11.72 11.82 11.92 12.02
Value 134.6 136.9 139.2 141.6 144.0

1. Fill in the blanks to complete the description of the track.
The track has ____ sides of the square and the distance around ____ complete circle(s).

Answer 1

Given:

The track is a square with a half circle on its left and right sides.

The area of the square is 128 square feet.

To find:

The length of the track.

Solution:

Let side length of the square be x.

Area of square is

`Area=(side)^2`

`128=x^2`

Taking square root on both sides.

`√(128)=x`

From the given table 127.7 is closed to 128. So,
`√(128)` is 11.3.

`x=11.3`

Diameter of circle = Side of square = 11.3.

The track has 2 sides of the square and the distance around 1 complete circle(s).

Radius of circle is

`(11.3)/(2)=5.65`

Length of the truck is sum of length of square and radii of two circles.

`Length =11.3+5.65+5.65`

`Length =22.6`

Therefore, the total length of the truck is 22.6 feet.