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 you answer the questions.
(insert tables here)
(insert track here)
1. fill in the blank to complete the description of the track.
the track has _ sides of the square and the distance around _ complete circle(s).

2.the length of one side of the square is the square root of its area. use the table to find the approximate length of one side of the square. explain how you used the table to find this information.

3. use your answers above to find the total length of the part of the track that is made up of sides of the square.

4. the circumference of (distance around) a circle is π time the diameter, or c=πd. a side of the square is the diameter of each half-circle.
in your answer to question 1, you gave the number of complete circles included in the track. use this answer ad c=πd to find the approximate length of the circular part of the track to the nearest tenth of a foot. use 3.14 for π and show your work.

5. find the approximate length of the track, including the straight and circular sections.

The length of the track is approximately 51.7 ft

The track has three sides of the square and the distance round a half of a complete circle

Step-by-step explanation:

The given track shape and measurements are;

The shape on the left side of the track  = Square

The shape on the right side of the track  = Half circle

The area of the square on the the left side of the track  = 128 square feet

Therefore, from the area, A, of a square of side length, s, which is s × s, and letting the side length of the square = s, we have;

Area of the square portion of the track = s × s = s² = 128 ft²

Therefore, s = √(128 ft²) = 8·√(2) ft.

Whereby the side length of the square is bounded by the diameter of the half circle, we have;

Length of the diameter of the half circle = s = 8·√(2) ft.

The length of the perimeter of the half circle = π·D/2 = π × 8·√(2)/2 = π × 4·√(2) ≈ 17.77 ft.

The perimeter of the track, which is the length of the track is made up of the three sides of the square opposite to the half circle and the circumference of the half circle.

Therefore;

The length of the track = 3 × 8·√(2) ft + π × 4·√(2) ft. = 4·√2×(π+6) ≈ 51.7 ft

The length of the track ≈ 51.7 ft

Which gives;

The track has three sides of the square and the distance round a half of a complete circle.