Let's say that we want to build a frame. As we layout the metal, how do we ensure it is square? There are several ways, one is to use the right angle calculations that you learned in an earlier chapter. The second is to use the Pythagorean theorem that states: the squares of each of the shorter lengths, added together, gives you the square of the hypotenuse (longest leg of the triangle). Mathematically, this is expressed as

Question

Let's say that we want to build a frame.  As we layout the metal, how do we ensure it is square?  There are several ways, one is to use the right angle calculations that you learned in an earlier chapter.  The second is to use the Pythagorean theorem that states: the squares of each of the shorter lengths, added together, gives you the square of the hypotenuse (longest leg of the triangle).  Mathematically, this is expressed as

In the Pythagorean theorem solution, the c2  is the corner to corner measurement.

However, there is an easier way, by using the 3 - 4 - 5 ratio.  So given the dimensions of 18" and 24" what would be the hypotenuse?

A hint: 18/3 is 6.

GPT 3.5 · Answer

To use the 3-4-5 ratio, we can multiply each side length by a common factor to maintain the ratio. In this case, we can multiply 3 by 6, and multiply 4 by 6. This gives us a new ratio of 18-24-30.

Therefore, the hypotenuse would be 30 inches.