Pythagorean triples are given by the formulas , , and . Use the formulas for the Pythagorean triples to find a right triangle with leg lengths of 16 and an odd number. Show all of your work for full credit.

Pythagorean triples are given by the formula:- AC² = AB² + BC²

The third side in the right triangle measures 23 units

Step-by-step explanation: The Pythagoras theorem as stated in the answer above is used in mathematics to solve for an unknown side(s) in any right angled triangle.

Pythagorean triples are so named because it refers to a right angled triangle in which the values of all three sides are always the same set of three numbers, and changing one of them changes everything completely. A very common Pythagorean triple is given as 3, 4 and 5. This means, the right angled triangle has sides measuring 3, 4 and 5. Hence to solve a right angled triangle with two sides given as 3 and 4 with the Pythagoras theorem is already half solved as the answer would always be 5.

Therefore, in a right triangle with leg lengths of 16, the first thing to note is that this a right isosceles triangle. We know this because a triangle with two legs having the same length is an isosceles triangle. That leaves us with the third side which is the hypotenuse. The Pythagoras formula just as stated above is given as follows;

AC² = AB² + BC²

Where AC is the hypotenuse (longest side), and AB and BC are the other two sides.

AC² = 16² + 16²

AC² = 256 + 256

AC² = 512

Add the square root sign to both sides of the equation

√AC² = √512

AC = 22.62741699...

AC ≈ 23

Therefore the Pythagorean triple as required by the question is given as

16, 16 and 23

or