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The problem presented is based on similar right triangles. In the smaller triangle, the drop is 1 cm over a horizontal distance of 30 cm. In the larger triangle, the horizontal distance is 700 cm, and we need to find the length \( \ell \) of the slanted pipe.

Since the triangles are similar, the ratio of corresponding sides will be the same. We can set up the following proportion based on the Pythagorean theorem:

\[
\frac{1}{30} = \frac{y}{700}
\]

Where:
- \( y \) is the vertical drop corresponding to the 700 cm horizontal distance.

Let's calculate the hypotenuse \( \ell \) using this ratio.The length \( \ell \) of the drainpipe is approximately 700.4 cm when rounded to the nearest tenth.

Do you need more details or have any further questions?

Here are 5 related questions for practice:
1. How would the length change if the horizontal distance were doubled?
2. If the drop increased to 2 cm per 30 cm, what would be the new length for a 700 cm horizontal distance?
3. Can you calculate the slope of the drainpipe in degrees?
4. What would the vertical drop be for a horizontal distance of 1 meter?
5. How would you calculate the length of the pipe if the slope was provided instead of the drop?

**Tip:** Always ensure that your ratios remain consistent when dealing with similar triangles!

A builder makes drainpipes that drop 1 cm over a horizontal distance of 30 cm. A certain drainpipe needs to cover a horizontal distance of 700 cm. What is the length of this drainpipe? Round your answer to the nearest tenth of a centimeter.

Explore how to calculate the length of a drainpipe using properties of similar triangles and the Pythagorean theorem. This problem covers the calculation of a hypotenuse in a real-world context, using a horizontal distance of 700 cm and a drop of 1 cm over 30 cm. Suitable for high school students in Grades 9-10.

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