A spiral built one right triangle at a time

One triangle gave a length that squares to 2. What length does the next triangle give?

How each stage is built

The next length squares to 3. Here is how each stage is built.

Start with two legs of 1 unit, at a right angle. The hypotenuse, the longest side, squares to 1 + 1 = 2. To square means to multiply a number by itself. Squares on the legs add to the square on the longest side.

Use that hypotenuse as one leg of a new right triangle. The other leg is a new 1. The new hypotenuse squares to 2 + 1² = 3.

Repeat this. Each new leg adds 1² = 1. So the square of the hypotenuse goes up by 1 each time.

Try the lab to finish this lesson.