Question 755861
{{{drawing(300,150,-1,13,-1,6,
rectangle(0,0,12,5),rectangle(0,0,0.5,0.5),
rectangle(0,4.5,0.5,5),rectangle(12,4.5,11.5,5),
rectangle(12,0,11.5,0.5),locate(-0.2,5.7,R),
locate(12,5.7,S),locate(12,-0.1,T),locate(-0.2,-0.1,U),
green(line(0,0,12,5)),green(line(0,5,12,0)),
locate(5.8,2.3,P)
)}}} Lines RT and SU are the diagonals of the rectangle.
Each diagonal divides the rectangle into two congruent right triangles.
The lengths of the legs of those right triangles are 5 and 12.
According to the Pythagorean theorem, the lengths of the hypotenuses of each triangle (the diagonals) are
{{{RT=SU=sqrt(5^2+12^2)=sqrt(25+144)=sqrt(189)=13}}}
So {{{RT=SU=13}}}
The diagonals of a rectangle (or any other parallelogram) bisect each other>
So {{{RP=PT=(1/2)RT}}} --> {{{RP=(1/2)13}}} --> {{{highlight(RP=6.5)}}}