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

1 Answer
Oscar L.
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=\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).

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