19.53 As shown in the figure, a square is divided into 24 rectangles (not necessarily of the same shape) by 5 lines parallel to one pair of opposite sides and 3 lines parallel to the other pair of opposite sides. If the sum of the perimeters of these 24 rectangles is 24, then the area of the original square is 
(A) 1.
(B) $\frac{9}{4}$.
(C) 4.
(D) $\frac{36}{25}$.
(2nd "Five Sheep Cup" Junior High School Mathematics Competition, 1990)
[Solution] Since when calculating the sum of the perimeters of these 24 rectangles, the sides of the rectangles contained within the original square are counted twice. Thus, if we let the side length of the original square be $x$, then
$$
4 x+2(5+3) x=24 \text{, i.e., } 20 x-24=0 \text{. }
$$

Solving for $x$ gives $x=\frac{6}{5}$, then $x^{2}=\frac{36}{25}$.
Therefore, the answer is $(D)$.