Question

1. a wheelchair ramp is being built to rise to a landing that is 2.4 m above the ground. building regulations say that the ramp can have a maximum rise of 2.5 cm per 30 cm of run.

a) what is the total run for the wheelchair ramp?
b) how long will the ramp be?

Explanation:

Step1: Convert units

The rise of the landing is \(h = 2.4m=240cm\).
The ratio of rise to run is \(r=\frac{2.5}{30}\).

Step2: Calculate the total run

Let the total run be \(x\). Using the proportion \(\frac{2.5}{30}=\frac{240}{x}\).
Cross - multiply: \(2.5x = 240\times30\).
Then \(x=\frac{240\times30}{2.5}=2880cm = 28.8m\).

Step3: Calculate the length of the ramp

Using the Pythagorean theorem \(l=\sqrt{h^{2}+x^{2}}\), where \(h = 2.4m\) and \(x = 28.8m\).
\(l=\sqrt{2.4^{2}+28.8^{2}}=\sqrt{5.76 + 829.44}=\sqrt{835.2}\approx28.9m\)

Answer:

a) The total run for the wheelchair ramp is \(28.8m\).
b) The length of the ramp is approximately \(28.9m\).