Use the pythagorean theorem to find the diagonal.
25+144=169, sqrt(169)=13, so the diagonal (OR) is 13.
The opposite sides of a rectangle are congruent. OA=5, AR=12
Let's find PO.
So, OA=PO*OR
Fill in known values.
52=PO*13.
Make PO the variable x.
25=13x
Divide by 13 on both sides.
x=25/13
25/13 = 1.9230769230769231
Round to the nearest hundredth.
x≈1.92
13-1.92 = 11.08, so the second part (PR) is 11.08
Now, to find PA we need to do the square root of 11.08*1.92.
11.08*1.92 = 21.2736, or 21.27
sqrt(21.27) = 4.6119410230400822, or approximately 4.61.