Math CentralQuandaries & Queries


Question from Trevor:

I am building a new house and wish to set it out on site with the use of profile boards and string. I want to be certain it is correct in terms of squareness. I have a vague idea that the square on the hypotenuse should be equal to the sum of the squares of the other two sides.

I get a little lost here and need some help. The building is a rectangle measuring 40x30 feet to exterior brickwork. I guess that the length of the hypotenuse should be exactly the square root of the combined squares of the two sides.

Using the above measurements could you give me calculations from nuts to soup as to the correct length of the diagonal. And what adjustments are needed if everything is not in accord.

Looking forward to hearing from you.



If the building is exactly 40x30, and a rectangle, then the hypotenuse should be exactly 50. If it is not a rectangle, one diagonal will be too long, the other too short.

If your quadrilateral has the right edge lengths, you can make it into a rectangle by physically shortening the long diagonal or stretching the short one.

Again, if the edge lengths are right, it is necessary and sufficient (for the frame to be a rectangle) to have the diagonals equal. This can be used for a "measuring-tape-free" construction using a cord to compare lengths.

Good Hunting!


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