The diagram below depicts a right triangle with an altitude, $\displaystyle {p}$, drawn from the vertex of its right angle to its hypotenuse. Solve for $\displaystyle {p}$ and reduce exactly, if necessary. 

[Graphs generated by this script: initPicture(-3.5,2.5,-.75,1.75);path([[0,0],[2,0],[0,1.25],[0,0],[-3,0],[0,1.25]]);path([[-3/10,27/24],[0,.95],[5/16,148/141]]);path([[0,.15],[.25,.15],[.25,0]]);text([.75,.75],$\displaystyle {o}$,aboveright);text([1,0],$\displaystyle {l}={2}$,below);text([-1.2,0],$\displaystyle {d}={3}$,below);text([-1,.75],$\displaystyle {t}$,aboveleft);text([0,.6],$\displaystyle {p}$,left)] 

Note: Should your answer require a square root type, 'sqrt(x)' in the answer bar to get $\displaystyle \sqrt{{{x}}}$.