Study guides › Level 7 · Geometry

Ladders and Pythagoras

Level 7 · Geometry · for questions like “A 13-foot ladder leans on a wall with its foot 5 feet out. How high does it reach?”

💡 The idea

The wall, the ground and the ladder make a right triangle. The ladder is the longest side.

🪜 The steps

1. Square the ladder's length, then take away the square of the other side you know.
2. Take the square root.

✏️ Worked examples

1. 13-foot ladder, foot 5 feet out: 169 − 25 = 144, and √144 = 12 feet high.

2. 25-foot ladder reaching 24 feet up: 625 − 576 = 49, and √49 = 7 feet out.

⚠️ Watch out

• Take away, don't add: the ladder is already the longest side.

🎯 Try these

1. 10-foot ladder, foot 6 feet out. How high?
2. 17-foot ladder reaching 15 feet. How far out?
3. 26-foot ladder, foot 10 feet out. How high?

Answers: 1) 8 2) 8 3) 24

This guide is also in the 10MathQ app: tap “📖 Study guide” after a question.