Example 3. As shown in Figure 3, through an internal point $P$ of $\triangle ABC$, three lines parallel to the three sides are drawn, resulting in three triangles $t_{1}, t_{2}$, and $t_{3}$ with areas 4, 9, and 49, respectively. Find the area of $\triangle ABC$.
(2nd American
Mathematical Invitational)
This example can directly apply the conclusion (4) of Theorem 2 to obtain
$$
S \triangle A B C=144
$$