Find the largest size of a bamboo that can be placed in a square of a…

The correct answer is Option (3) → 26 m

The longest straight line that fits inside a square is its diagonal, which joins two opposite corners. For a square of side \(a\), the diagonal is \(a\sqrt{2}\).

• The area gives the square of the side: \(a^2=338\,\mathrm{m^2}\)

• Square of the diagonal, from \((a\sqrt{2})^2=2a^2\): \(2\times338=676\)

• Length of the diagonal, the longest bamboo: \(\sqrt{676}=26\) m

Tip: \(13\sqrt{2}\) m (Option 2) is the side of the square, since \(\left(13\sqrt{2}\right)^2=338\); the bamboo laid along the diagonal is longer.