10.122. The larger base of the trapezoid has a length of 24 cm (Fig. 10.113). Find the length of its smaller base, given that the distance between the midpoints of the diagonals of the trapezoid is 4 cm.
Solution.

$A E=E C ; D F=F B, K E=D C / 2 ; F T=D C / 2 ; D C=x, K T=2 K E+E F=$ $=x+4$. On the other hand, $K T=\frac{x+24}{2}$. Solving the equation $x+4=\frac{x+24}{2}$, we get $x=16$ (cm).

Answer: $16 \mathrm{~cm}$.