Brian borrowed a 20-foot extension ladder to paint his house. For a stable footing he sets the base of the ladder 6 feet out from the wall. About how far up the wall will the top of the ladder reach?

1. The wall, the ground, and the ladder form a right triangle, with the 20-foot ladder as the hypotenuse. 2. The Pythagorean Theorem gives a squared plus b squared equals c squared. 3. Substitute the known lengths: 6 squared plus h squared equals 20 squared. 4. Compute the squares: 36 plus h squared equals 400. 5. Subtract 36 from both sides: h squared equals 364 square feet. 6. Take the square root: h equals the square root of 364, which is about 19.1 feet up the wall. 7. About 14.0 feet subtracts 6 from 20 directly, skipping the squaring that the theorem requires. 8. About 26.0 feet adds the two lengths, which would need a ladder longer than the one Brian borrowed. 9. About 20.9 feet adds 36 to 400 instead of subtracting, mixing up which side of the equation the hypotenuse sits on. _Source: OpenStax Prealgebra (CC BY 4.0), Ch 9 "Math Models and Geometry", section 9.3 Use Properties of Angles, Triangles, and the Pythagorean Theorem_