# The perimeter of the quadrilateral ABCD is 100 cm. The AB side is 41 cm, the BC side is 18 cm shorter

**The perimeter of the quadrilateral ABCD is 100 cm. The AB side is 41 cm, the BC side is 18 cm shorter than the AB side, but 6 cm longer than the CD side. Find the length of the AD side.**

1. First, find the length of the BC side. It is shorter than the AB side by 18 cm. Let’s calculate it:

BC = AB – 18;

BC = 41 – 18;

BC = 23 (cm).

2. Now let’s find the length of the CD side. If the BC side is 6 cm longer than it, then the CD side is 6 cm shorter than the BC. Let’s calculate it:

CD = BC – 6;

CD = 23 – 6;

CD = 17 (cm).

3. Finally, it was the turn to find out the length of the AD side. We subtract the three found sides from the length of the perimeter. We get the fourth:

AD = P – AB – BC – CD;

AD = 100 – 41 – 23 – 17;

AD = 19 (cm).

Answer: the length of the AD side is 19 cm.