The shortest piece

1. Step 1 · Work out the opposite

   $\displaystyle \text{every piece is longer than } 20 \text{ cm}$

   "At most 20 cm" has many cases; "all over 20 cm" is one region, so find it and take it from 1.

2. Step 2 · Give each piece 20 cm first

   $\displaystyle 100 - 3 \times 20 = 40 \text{ cm}$

   If every piece is over 20 cm, take 20 cm off each. What’s left is a random split of 40 cm.

3. Step 3 · Chance every piece is over 20 cm

   $\displaystyle \left(\frac{40}{100}\right)^{2} = \frac{4}{25}$

   The region in the square is the full picture shrunk to 40% across and 40% up, so its area is 0.4².

4. Step 4 · Shortest is 20 cm or less

   $\displaystyle 1 - \frac{4}{25} = \frac{21}{25}$

   Everything outside the blue triangles has a piece of 20 cm or less.

Answer$\displaystyle \frac{21}{25} = 84\%$