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
[tex]Area=(side)^2[/tex]
[tex]128=x^2[/tex]
Taking square root on both sides.
[tex]\sqrt{128}=x[/tex]
From the given table 127.7 is closed to 128. So, [tex]\sqrt{128}[/tex] is 11.3.
[tex]x=11.3[/tex]
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
[tex]\dfrac{11.3}{2}=5.65[/tex]
Length of the truck is sum of length of square and radii of two circles.
[tex]Length =11.3+5.65+5.65[/tex]
[tex]Length =22.6[/tex]
Therefore, the total length of the truck is 22.6 feet.
