Question

Tyrese buys potting soil every January to plant vegetables in his garden. This year he bought 15 25-pound bags of potting soil. He must push them up a 6- foot-high ramp to his truck. The horizonal distance from the base of the ramp to the truck is 8 feet. Apply a Pythagorean triple to find the length of the ramp.(1 point) feet

Answer 1

To find the length of the ramp using the Pythagorean theorem, we can model the ramp, the height of the ramp, and the horizontal distance as a right triangle, where:

- \(a\) is the height of the ramp (6 feet),
- \(b\) is the horizontal distance (8 feet),
- \(c\) is the length of the ramp (the hypotenuse).

According to the Pythagorean theorem:
\[
c^2 = a^2 + b^2
\]

Substituting the values we have:
\[
c^2 = 6^2 + 8^2
\]
\[
c^2 = 36 + 64
\]
\[
c^2 = 100
\]

Now, taking the square root of both sides to find \(c\):
\[
c = \sqrt{100} = 10
\]

Thus, the length of the ramp is **10 feet**.