Finding a shorter side
A 13 m ladder leans on a wall. Its foot, on the ground, is 5 m from the wall. How far up the wall does it reach?
Step 1 of 4
- The ladder, the ground and the wall.
- Known: the ladder is 13, the foot is 5.
- The wall is the side left to find.
- 13 × 13 − 5 × 5 = 169 − 25 = 144. 12 × 12 = 144, so the wall is 12.
The ladder reaches 12 m up the wall.
Rule: Square the long side. Square the short side you know. Subtract the smaller from the bigger. Hunt for the number that squares to that. Hunting means trying numbers until one squares to the result.
The long side's square is the sum of the two short squares. So take the known short square away from it.
Check by adding: 144 + 25 = 169, and 169 = 13 × 13. Always take the short square from the long square. The long side's square is the bigger number.
Drag the foot of the ladder. See how high it reaches.
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