3. $A B C D$ is a parallelogram with $\angle D$ obtuse. $M, N$ are the feet of perpendiculars from $D$ to $A B$ and $B C$ respectively. If $D B=D C=50$ and $D A=60$, find $D M+D N$.
$A B C D$ is a parallelogram, where $\angle D$ is obtuse. $M$ and $N$ are the feet of the perpendiculars from $D$ to $A B$ and $B C$ respectively. If $D B=D C=50$ and $D A=60$, find $D M+D N$.
3. 88
3. Note that $N$ is the mid-point of $B C$, so $N B=N C$ $=30$. By Pythagoras' Theorem, we have
$$
D N=\sqrt{50^{2}-30^{2}}=40 \text {. }
$$

Computing the area of $A B C D$ in two ways, we get
$$
60 \times 40=50 \times D M,
$$
which gives $D M=48$. It follows that
$$
D M+D N=48+40=88 \text {. }
$$