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

Question

GPT-4o mini · Answer

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.