Question 148693
This is a good problem. Analyzing it, that 24 meters from the center of the park to the closest point of this straight path cutting is only possible if it is <font><font size=4>perpendicular</font>. Draw it on a diagram and you'll see why.
Now that forms two oppposite right triangle, with equal measurements and hypotenuse of each is the radius = 40 meters---- mark "c". Also mark "a" the 24 meters, from the center perpendicular to the middle of the path cutting.
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Focusing on 1 triangle, we'll get half of the total length of the path cutting then right?---- mark this  as {{{highlight(b)}}} ----->unknown oks?
Therefore by Pythagorean Theorem, {{{c^2=a^2 + b^2}}}
{{{b^2=c^2-a^2}}}
{{{b=sqrt(40^2-24^2)}}}
{{{b=sqrt(1024)}}}
{{{b=32meters}}}
Since that's only 1 triangle showing half of the length, we multiply it by 2 to get the full length of the path cutting, {{{32meters*2=64meters}}} ---> final answer.
<font><fonzt size=4><b>Thank you
Jojo</font>