chris builds a ramp for his home the ramp starts 24 horizontal feet from the door and rises a total of 2 ft

Chris has built a ramp that starts 24 feet horizontally from the door and rises 2 feet in height. This situation describes a right triangle, where:

- The horizontal distance (run) is 24 feet.
- The vertical rise is 2 feet.
- The length of the ramp would be the hypotenuse of this right triangle.

To find the length of the ramp (hypotenuse), we can use the Pythagorean theorem:

\[
c^2 = a^2 + b^2
\]

Where:
- \( c \) is the length of the ramp (hypotenuse),
- \( a = 24 \) feet (horizontal distance),
- \( b = 2 \) feet (vertical rise).

Now, let's calculate the length of the ramp:

\[
c^2 = 24^2 + 2^2
\]
\[
c^2 = 576 + 4
\]
\[
c^2 = 580
\]
\[
c = \sqrt{580} \approx 24.08 \text{ feet}
\]

So, the length of the ramp is approximately **24.08 feet**.

Would you like more details or have any questions about this?

Here are 5 related questions to expand this concept:
1. How would the ramp length change if the vertical rise was 3 feet instead of 2?
2. What is the slope of the ramp in this case?
3. How long would the ramp be if the horizontal distance was halved?
4. How does increasing the horizontal distance affect the overall ramp length?
5. What angle does the ramp make with the ground?

**Tip**: The slope of a ramp is often expressed as "rise over run." You can use this ratio to check accessibility standards for ramps!

Learn how to calculate the length of a ramp that starts 24 feet from a door and rises 2 feet using the Pythagorean Theorem. This problem involves applying geometric concepts to find the hypotenuse of a right triangle, suitable for students in Grades 6-8.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation