Calculating the Length of a Walk-Up Ramp Using the Pythagorean Theorem

Imagine a scenario where a walk-up ramp moves horizontally 20 feet while rising 6 feet. This situation can be depicted as a right triangle, where the horizontal run represents one of the legs, and the vertical rise represents the other leg. To find the actual length of the ramp, we need to calculate the hypotenuse of this right triangle.

Using the Pythagorean Theorem

The Pythagorean theorem is a fundamental principle in geometry, which states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b). The theorem can be expressed as:

c2  a2   b2

In this scenario, the horizontal run (a) is 20 feet, and the vertical rise (b) is 6 feet. Using the Pythagorean theorem, we can calculate the length of the ramp (c) as follows:

c2  202   62

c2  400   36

c2  436

c  √436

Using a calculator to find the square root of 436, we get:

c ≈ 20.88 ft

Rounding to the nearest tenth, the length of the ramp is approximately 20.9 feet.

Visualizing the Ramp

The ramp can be visualized as the hypotenuse of a right triangle with legs of 20 feet and 6 feet. By applying the Pythagorean theorem:

ramp length  √(202   62)

ramp length  √(400   36)

ramp length  √436

Calculating this, we find:

ramp length ≈ 20.88 ft

Rounded to the nearest tenth, the ramp length is 20.9 feet.

Conclusion

In this scenario, the length of the walk-up ramp, which moves horizontally 20 feet while rising 6 feet, is approximately 20.9 feet, when rounded to the nearest tenth. This application of the Pythagorean theorem is a practical and efficient way to determine the length of a ramp in real-world situations.