Question

Use the Pythagorean Theorem, what is the length of the hypotenuse in a right triangle whose legs are 3 and 4?

Answer 1

5 units. This is a very famous triangle.

Explanation:

If `a,b` are the lehs of a right triangle and `c` is the hypoteneuse, then the Pythagorean Theorem gives:

`c^2=a^2+b^2`

Then since the side lengths are positive:

`c=\sqrt{a^2+b^2}`

Put in `a=3, b=4`:

`c=\sqrt{3^2+4^2}`
`=\sqrt{25}=5`.

The fact that a triangle with sides of 3, 4, and 5 units is a right triangle has been known since at keast the ancient Egyptians. This is the Egyptian triangle, believed to be used by the ancient Egyptians to construct right angles -- for example, in the Pyramids (https://nrich.maths.org/982).