A square field has an area of \( 2 \frac{1}{2} \) hectares. Find the length of a side in metres, to the nearest metre. \( \begin{array}{lll}\text { A } 16 \mathrm{~m} & \text { B } 50 \mathrm{~m} & \text { C } 158 \mathrm{~m} \\ \text { D } 500 \mathrm{~m} & \text { E } 1581 \mathrm{~m} & \end{array} \)

To solve for the length of a side of the square field, we start by converting the area from hectares to square meters. Since 1 hectare is equal to 10,000 square meters, \( 2 \frac{1}{2} \) hectares is equal to \( 2.5 \times 10,000 = 25,000 \) square meters. Now, since the area \( A \) of a square is given by the formula \( A = s^2 \) (where \( s \) is the length of one side), we can find the length of a side by taking the square root of the area: \[ s = \sqrt{25,000} \approx 158.11 \text{ meters} \] Rounding to the nearest meter, the length of a side is approximately 158 meters, making the answer C: 158 m. For a bit of context, the concept of area has been around since ancient civilizations used geometry for land measurement and architecture. Think of the Egyptians calculating the area of their fields along the Nile! Also, when dealing with problems involving units, always pay attention to conversions. Common mistakes include forgetting to convert hectares to square meters, or miscalculating square roots. Always double-check your units to avoid mix-ups!