Question 126320
Just plug in the given value for length and do the arithmetic.


{{{8T^2=pi^2L}}}


{{{8T^2=10*pi^2}}}


{{{T^2=(10/8)*pi^2}}}


{{{T=sqrt((10/8)*pi^2)}}}


{{{T=pi*sqrt(10/8))}}}.


Rationalize the denominator:


{{{T=pi*(sqrt(10)/sqrt(8))(sqrt(8)/sqrt(8))=pi*(sqrt(80)/8)=(4*pi*sqrt(5))/8=red((pi*sqrt(5))/2)}}}.


Now you can use the calculator to find the approximate decimal value, or leave it alone for the exact answer