Question

a hobbyist makes all of their ramps with a base to height ratio of 14 : 1 in his workshop, as shown in the diagram below, which is not drawn to scale: diagram with base labeled 14 and height labeled 1
a certain ramp needs to have a height of 0.8 meters.
diagram with height labeled 0.8 m and base labeled ℓ
what is the length ℓ of this ramp?
round your answer to the nearest hundredth of a meter.
answer box m
make expression button

Explanation:

Step 1: Understand the ratio

The ratio of base to height is \(14:1\). This means for every 1 unit of height, the base (length of the ramp) is 14 units.

Step 2: Set up the proportion

Let \( \ell \) be the length of the ramp. The height of the ramp is \( 0.8 \) meters. Using the ratio, we have the proportion \( \frac{\ell}{0.8}=\frac{14}{1} \).

Step 3: Solve for \( \ell \)

To find \( \ell \), we can cross - multiply. From \( \frac{\ell}{0.8}=\frac{14}{1} \), we get \( \ell=14\times0.8 \).
Calculating \( 14\times0.8 = 11.2 \).

Answer:

\( 11.2 \)