10.141. Determine the lateral sides of an isosceles trapezoid if its bases and area are respectively $8 \mathrm{~cm}, 14 \mathrm{~cm}$, and $44 \mathrm{~cm}^{2}$.
Solution.

Let $B C=8, A D=14$ (Fig. 10.127). Draw $B L \perp A D, C M \perp A D$. $S_{A B C D}=\frac{B C+A D}{2} B L$. Therefore, $B L=\frac{2 S_{A B C D}}{B C+A D}=4$ (cm). According to the condition, $A B=C D, B L=C M$. Thus, $A L=M D=\frac{A D-L M}{2}=3$ (cm). Then $A B=\sqrt{\dot{B} L^{2}+A L^{2}}=\sqrt{16+9}=5(\mathrm{~cm})$.

Answer: $5 \mathrm{~cm}$.