Setting Out a Return Corner When the Diagonals Do Not Agree
You are setting out a rectangular single-storey extension, 6.4 m by 4.2 m externally, on a concrete raft. You strike the first long line along the existing building and square off the first corner with a 3-4-5 triangle. You then measure the two long sides and the two short sides and they agree with the drawings within 5 mm. But when you check the diagonals, one reads 7.660 m and the other reads 7.700 m - a 40 mm difference. The bricklayer says a 40 mm difference over 7.7 m is 'nothing' and wants to start the footings.
1. Explain what the diagonal discrepancy tells you and whether the setting out is acceptable.
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For a true rectangle, the diagonals must be equal. The expected diagonal is the square root of (6.4² + 4.2²) = √(40.96 + 17.64) = √58.60 ≈ 7.655 m. One diagonal at 7.660 m is close to that; the other at 7.700 m is 45 mm over.
Equal opposite sides do not prove a rectangle - a parallelogram also has equal opposite sides. The 40 mm diagonal difference means the setting out is a parallelogram, not a rectangle: the corners are not square. Over a 7.7 m diagonal, 40 mm is a significant error and will show up as out-of-square corners and a tapering wall, and it will affect the roof and any fitted units.
The setting out is not acceptable. It must be corrected before any footings are poured or any brick is laid.
2. Describe how you would correct the setting out and verify it before proceeding.
Read the worked answer
Correction method:
- Hold the two lines that are known good (the existing building line and one long side) and adjust the opposite long side and the short returns until both diagonals match.
- Work from the corner that is known square: move the far corner along the short return until the diagonals agree. Re-measure both diagonals after each adjustment; they should converge on the same value, about 7.655 m.
- Re-check all four sides after the diagonals agree, because moving a corner changes side lengths.
- Verify squareness independently with a 3-4-5 triangle at each corner, not just one.
- Mark the corrected corners with permanent pins or profiles set clear of the excavation, and record the final diagonal readings in the site diary.
- Only then set out the footings.
A useful check: if the diagonals agree and opposite sides agree, the shape is a rectangle, and the corners can be confirmed with the triangle method.