The remainder is the integer left over after dividing one integer by another. The quotient is the quantity produced by the division of two numbers.
Hope that helped !
The thing about that problem is that when the circle is inscribed inside that triangle, the side measures created are doubled. By that I mean that the 9 on the top right is also the measure of the top left. Same thing for the 13 and the 16. The lower left unmarked side length is 13, the lower right side length is 16. Now add it all up: 9+9+13+13+16+16