To set a layout of a house room by offset method using Pythagoras’ Theorem.

Object: To set a layout of a house room by offset method using Pythagoras’ Theorem.

Theory: 3-4-5 method:

If a triangle has sides measuring 3, 4, and 5 ft (or any other unit), it must be a right triangle with a 90° angle between the short sides. If you can find this triangle in your corner, you know the corner is square. This is based on the Pythagoras’ Theorem from geometry: A2 + B2 = C2 for a right triangle. C is the longest side (hypotenuse), and A and B are the two shorter “legs.”

NOTE: Instead of 3 m, 4 m, and 5 m a multiple can be chosen: e.g. 6 m, 8 m, and 10 m or e.g. 9 m, 12 m, and 15 m.

Instruments required:

1. 50 m (166’) measuring tape
2. 10 Arrows
3. 4 Ranging Rods

Procedure:

1. To set the boundaries of the house first, measure 40 feet along one side. This is the base line. Fix two ranging rods at the ends of the base line, respectively.

First rod is at the zero mark and the other at 40’ mark.

1. Measure 30’ along the other side. Measure along the second side, at hopefully a 90° angle to the first. The reading on the tape should be 70’. Mark this point with an arrow.
2. Measure the hypotenuse i.e. distance between the rod at zero mark and the arrow.
   • If the reading shown on the tape is 120’ (i.e. hypotenuse is 50’), your corner is square. Remove the arrow and fix another rod at the same point.
   • If the reading shown on the tape is less than 120’, your corner is less than 90°. Move the sides apart from the end of 30’. Remove the arrow and fix another rod at the same point.
   • If the reading shown on the tape is more than 120’, your corner has a measurement of more than 90°. Bring the sides closer together from the end of 30’. Remove the arrow and fix another rod at the same point.
3. Once you’ve got a square corner, you can check the room’s other three corners by repeating the above procedure to ensure they are the same. Fix the fourth-ranging rod at the fourth corner of the house.
4. Now, for setting the dimensions for the Room 1, measure 20’ on the base

line and mark with an arrow.

1. Repeat Step 2 with 15’ measured at the second side (on the 30’ line). The reading on the tape should be 35’. Mark with an arrow.
2. Repeat Step 3 with 25’ measured as hypotenuse. The reading on the tape should be 60’. If not, adjust as mentioned above in the bullet points.
3. Repeat Step 4. Fix an arrow on the fourth corner of the room.
4. Repeat Steps 5, 6, 7, and 8 for Room 2 adjacent to Room 1 using the same dimensions.
5. Now, for setting the dimensions for Room 3, measure 10’ on the remaining 20’ base line and mark with an arrow.
6. Repeat Steps 6, 7, and 8. Measure the second side as 15’, so that the reading on the tape is 25’. Measure the hypotenuse as 18.03’, so that the reading shows 43’ and 3 out of 8 parts of an inch.
7. As Room 4 is already there below Room 3, check its dimensions again by using the 3-4-5 method. It must have the same dimensions as Room 3.
8. As Room 5 is already there below Room 2, check its dimensions by the 3-4-5 method. It must have the same dimensions as Rooms 1 and 2.

Dimensions according to 3-4-5 Method:

Observations in the field: