3. An agricultural company owns a rectangular plot of land with an area of 800 m2. It is known that the length is twice as long as the width. If the agricultural company wants to place a fence on the diagonal of said land. How many meters of fence are needed? (2 points).

1. Base: el área del rectángulo \( A \) es igual a \( 800 \) m².

length \times width = 800

2. Denotamos el ancho como \( x \) y el largo como \( 2x \), obteniendo así:

2x^2 = 800

3. Resolviendo para \( x \):

x^2 = 400

x = \sqrt{400}

x = 20

4. Por lo tanto, el ancho es \( 20 \) metros y el largo es \( 40 \) metros.

5. Usamos el teorema de Pitágoras para encontrar la diagonal:

diagonal^2 = 40^2 + 20^2

diagonal^2 = 1600 + 400

diagonal^2 = 2000

diagonal = \sqrt{2000}

diagonal = 20\sqrt{5}

Answer:
20\sqrt{5} \text{ metros}