We first draw the triangle in the coordinate axis, as shown in the picture.
We then circumscribe a rectangle (in fact a square) to this triangle, and we notice that each of the sides is the hypotenuse of a right triangle:
this triangles, as can be seen from the picture, have sides of length:
{5, 3}, {2, 3}, and {5, 2}.
By the pythagorean theorem, the sum of these three hypotenuses is:
[tex] \sqrt{5^2+3^2}+ \sqrt{2^2+3^2}+ \sqrt{5^2+2^2}\\\\= \sqrt{34}+ \sqrt{13}+ \sqrt{29}\\\\\approx 5.83+ 3.6+5.385\\\\\approx14.8 [/tex]
Answer: 14.8 (units)
