A builder makes drainpipes that drop 1 cm over a horizontal distance of 30 cm to prevent clogs. See the
diagram below, which is not drawn to scale:
A certain drainpipe needs to cover a horizontal distance
of 700 cm
What is the length l of this drainpipe?
Round your answer to the nearest tenth of a centimeter
cm

700.4 cm

Step-by-step explanation:

This involves two similar triangles.

Both triangles are right triangles.

One has legs measuring 1 cm and 30 cm. We can find the hypotenuse by using the Pythagorean theorem.

(1 cm)^2 + (30 cm)^2 = c^2

c^2 = 901 cm^2

c = sqrt(901) cm

The second triangle has one leg with length 700 cm. This leg corresponds to the 30-cm leg in the other triangle. Since the triangles are similar, we can use a proportion to find the hypotenuse of the second triangle.

(30 cm)/(700 cm) = [sqrt(901) cm]/x

3/70 = sqrt(901) cm/x

3x = 70 * sqrt(901) cm

x = 70 * sqrt(901) cm/3

x = 700.4 cm

700.4 cm