Three similar pieces of timber of length 240cm, 320cm, are cut into two equal pieces. Find the largest possible area of a square which can be made from any of the three pieces (3m)

Each original piece of timber is cut into two equal pieces.
For an original piece of length 240 cm:

For an original piece of length 320 cm:

The problem implies we have pieces of these lengths available after cutting.

To form a square, four equal sides are needed. The perimeter of the square will be equal to the length of the timber piece used. If $s$ is the side length of the square, then $4s = \text{length of timber piece}$.

For a 120 cm long piece:

For a 160 cm long piece:

The area of a square is given by the formula $A = s^2$.

For the square made from a 120 cm piece:

For the square made from a 160 cm piece:

Comparing the two possible areas, $900 \text{ cm}^2$ and $1600 \text{ cm}^2$, the largest possible area is $1600 \text{ cm}^2$.