CLC Construction Math & Site Layout

Question 1

Using the 3-4-5 method, what diagonal measurement confirms a square corner when the two legs measure 6 ft and 8 ft?

Accepted Answer

10 ft

Answer

A 6-8-10 triangle is a multiple of the 3-4-5 right triangle. The diagonal is 10 ft (6² + 8² = 100) when the corner is exactly 90°.

Question 2

What is the sum of 14'-7 3/8" and 8'-4 5/8"?

Accepted Answer

23'-0"

Answer

The fractions add to 7 3/8 + 4 5/8 = 12 inches, which carries over as 1 ft. The result is 14 + 8 + 1 = 23'-0".

Question 3

After laying out a rectangular building with string lines, how do you check that the layout is square?

Accepted Answer

Measure that the two diagonals are equal

Answer

A rectangle has equal diagonals only if its corners are square. Opposite sides can be equal on a parallelogram that is not square.

Question 4

What is the board-foot volume of one 2x4x10 piece of lumber (nominal dimensions)?

Accepted Answer

6.67 bf

Answer

Board feet = thickness (in) × width (in) × length (ft) ÷ 12 = 2 × 4 × 10 ÷ 12 ≈ 6.67 bf.

Question 5

A roof has a 6-in-12 pitch and the building run (half-span) is 12 ft. What is the approximate rafter length, excluding overhang?

Accepted Answer

13.42 ft

Answer

Rise = 12 ft × 6/12 = 6 ft. Rafter length = √(12² + 6²) = √180 ≈ 13.42 ft.

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