161. In an isosceles triangle with a side length of 10 and a base of 12, inscribe a square.
161. Height $B G=\sqrt{B C^{2}-G C^{2}}=$ $=\sqrt{100-36}=8 ; \triangle B D E \subset \triangle A B C$ (fig. 44 ).

If $D E=\boldsymbol{x}$, then $x:(8-x)=12: 8$; $20 x=96 ; x=4 \frac{4}{5}$.

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