Answer
The length of one side of the patio is $4m-9$.
Work Step by Step
$16m^{2}-72m+81=$
...write first and last terms as squares.
$=(4m)^{2}-72m+(9)^{2}$
...does middle term equal $2ab$?
$72m=2\cdot(4m)\cdot(9)$
$=(4m)^{2}-2\cdot(4m)\cdot(9)+(9)^{2}$
...write as the square of a binomial.
$=(4m-9)^{2}$
The length of one side of the patio is $4m-9$.
