Question

1. a building has a ramp to its front doors to accommodate the handicapped. if the distance from the building to the end of the ramp is 16 feet and the height from the ground to the front doors is 8 feet, how long is the ramp?

Explanation:

Step1: Apply Pythagorean theorem

Let the length of the ramp be \(l\). According to the Pythagorean theorem \(a^{2}+b^{2}=c^{2}\), where \(a = 8\) (height), \(b=16\) (horizontal distance), and \(c = l\) (ramp length). So \(l^{2}=8^{2}+16^{2}\).

Step2: Calculate \(8^{2}+16^{2}\)

\(8^{2}=64\), \(16^{2}=256\). Then \(8^{2}+16^{2}=64 + 256=320\).

Step3: Find \(l\)

Since \(l^{2}=320\), then \(l=\sqrt{320}\). Simplify \(\sqrt{320}=\sqrt{64\times5}=8\sqrt{5}\approx 8\times2.24 = 17.92\) feet.

Answer:

The length of the ramp is \(8\sqrt{5}\approx17.92\) feet.