Question

A waterslide is 4.2 m high and has a support 2.4 m tall. If a student reaches this support when she is 3.1 m down the slide, how long is the slide?

Answer 1

Refer to the diagram shown below.

The triangles ΔABC and ΔADE are similar because of AAA.
Therefore
$\frac{AC}{AE} = \frac{BC}{DE} \\\\ \frac{x}{x+3.1} = \frac{2.4}{4.2} = 0.5714 \\\\ x = 0.5714(x+3.1)$
0.4286x = 1.7713
x = 4.133 m

The length of the slide is x + 3.1 = 4.133 + 3.1 = 7.233 m

Answer: 7.2 m (nearest tenth)