1. The perimeter of quadrilateral $A B C D$ is 100 cm. The length of side $A B$ is 41 cm, side $B C$ is 18 cm shorter than side $A B$, but 6 cm longer than side $C D$. Find the length of side $A D$.
1. The first method of solving.
1) $41-18=23$ cm - the length of side $B C$;
2) $23-6=17$ cm - the length of side $C D$;
3) $41+23+17=61$ cm - the sum of sides $A B, B C$, and $C D$;
4) $100-61=19$ cm - the length of side $A D$.

The second method of solving. Another approach can be used to solve this problem. First, determine the tripled length of side $A B$. Then, subtract the excess length from the obtained number

$$
41 \times 3-(18 \times 2+6)=81 \text {. }
$$

On the last step, determine $A D$

$$
100-81=19
$$

To make this solution more understandable, it is necessary to make a brief record of the problem's conditions.

Answer: the length of side $A D$ is 19 cm.