Where it is used
A small window gate is 24 cm across and 7 cm high. How long is its diagonal bar?
Step 1 of 3
- The small gate: 24 across, 7 high, and the diagonal bar.
- Known sides: 24 and 7.
- 24 × 24 + 7 × 7 = 576 + 49 = 625. 25 × 25 = 625, so the bar is 25.
The diagonal bar is 25 cm long.
Rule: draw the triangle and find the square corner. Name the side across from it — the long one. Add the squares of the short sides to find the long side. Subtract a short square from the long square for a short side. Then hunt for the match. To hunt is to try numbers until one squares to the result.
A brace is a diagonal bar that keeps a frame stiff.
| The job | Known sides | Add or subtract | Answer |
|---|---|---|---|
| Ladder 10, foot 6, find the reach | long and short | take: 100 − 36 | 8 |
| Field 9 by 12, find the walk across | two short | add: 81 + 144 | 15 |
| Charpai frame 12 by 16, find the brace | two short | add: 144 + 256 | 20 |
Watch out!
A brace spans 6 across and 8 up: add, 36 + 64 = 100. A ladder is 10 long, foot 6 out: subtract, 100 − 36 = 64. Same three numbers, different jobs.
Pick add or subtract. Then check your pick.
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