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This problem involves calculating the length of a pipe that is placed at an incline, where the horizontal distance is given as 700 cm, and for every 30 cm of horizontal distance, the pipe drops by 1 cm.

We can model this as a right triangle, where:

- The horizontal distance is the base, \(700 \, \text{cm}\).
- The vertical drop follows the ratio \( \frac{1 \, \text{cm}}{30 \, \text{cm}} \), so for 700 cm, the vertical drop will be:
  \[
  \text{Vertical drop} = \frac{700}{30} = 23.33 \, \text{cm}.
  \]
- The length of the pipe, \( \ell \), is the hypotenuse of the triangle.

We will use the Pythagorean theorem to find \( \ell \):
\[
\ell = \sqrt{(700)^2 + (23.33)^2}.
\]

Let me calculate this for you.The length \( \ell \) of the pipe is approximately \( 7.00 \, \text{m} \) when rounded to the nearest hundredth of a meter.

Would you like further details on this solution or have any questions?

Here are some related questions you might find interesting:
1. How would the length change if the horizontal distance were 1000 cm?
2. What would happen if the vertical drop increased to 2 cm per 30 cm?
3. How can you calculate the angle of incline for the pipe in this scenario?
4. What is the vertical drop over a 1000 cm horizontal distance, maintaining the same ratio?
5. How does the Pythagorean theorem help solve problems involving right triangles?

**Tip:** Always remember to check units (meters, centimeters, etc.) when solving problems involving distance, to avoid confusion!

Un constructor coloca tuberías de drenaje que descienden 1 cm cada 30 cm horizontales, para evitar obstrucciones. ¿Cuál es la longitud l de una tubería que debe cubrir una distancia horizontal de 700 cm? Redondea tu respuesta a la centésima de metro más cercana.

Aprende a calcular la longitud de una tubería inclinada utilizando el Teorema de Pitágoras. Esta lección cubre conceptos de geometría y trigonometría, adecuados para estudiantes de grados 8-10. Incluye un ejemplo práctico con una distancia horizontal de 700 cm y un descenso de 1 cm por cada 30 cm horizontales.

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