Pavement

Calculate the length of the pavement that runs through a circular square with a diameter of 40 m if distance the pavement from the center is 15 m.

Result

x =  26.458 m

Solution:

D=40 m h=15 m  r=D/2=40/2=20 m  (x/2)2+h2=r2  x=2⋅ r2−h2=2⋅ 202−152≐10 7≐26.4575≐26.458 mD=40 \ \text{m} \ \\ h=15 \ \text{m} \ \\ \ \\ r=D/2=40/2=20 \ \text{m} \ \\ \ \\ (x/2)^2 + h^2=r^2 \ \\ \ \\ x=2 \cdot \ \sqrt{ r^2-h^2 }=2 \cdot \ \sqrt{ 20^2-15^2 } \doteq 10 \ \sqrt{ 7 } \doteq 26.4575 \doteq 26.458 \ \text{m}

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