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

##### 1 Answer
Aug 3, 2016

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:

$c = \setminus \sqrt{{a}^{2} + {b}^{2}}$

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

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

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).