The Pythagorean Theorem allows you to find an unknown side length in a right triangle by
applying the equation a² + b2 = c2. In this equation, a and b are the lengths of the sides
adjacent to the right angle (the legs) and c is the length of the side opposite the right angle
(the hypotenuse).
The sides a and b of a right triangle may be any length, but
often c turns out to be an irrational number, like V13. It's
helpful to recognize a few sets of side lengths that are whole
numbers. These lengths are known as Pythagorean triples.
A few Pythagorean triples are listed here. Any whole-number
multiple of these side lengths is also a Pythagorean triple.
3,4,5 5, 12, 13 8, 15, 17
7,24,25 20,21,29
What are some
Pythagorean triples based
on multiples of the side
lengths of a triangle with
sides 3, 4, and 5?
The Pythagorean Theorem is a powerful tool for finding lengths
that are not easily measured, such as the distance across a pond.
It is also often used to find lengths in geometric figures that are
not right triangles but can be decomposed into right triangles.
And it can even be used to find lengths in three-dimensional
figures, as in the rectangular prism shown here.
Reflect
1 Is the length of the hypotenuse of a right triangle with legs that measure 4 cm and 5 cm
a rational number or an irrational number? Justify your answer.