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

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

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Answer 1 · 2016-08-03T01:57:49

5 units. This is a very famous triangle.

Explanation:

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

$c^{2} = a^{2} + b^{2}$ $c^2=a^2+b^2$

Then since the side lengths are positive:

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

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

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

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

1 Answer

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