Does the set of numbers represent a Pythagorean triple?
14,20,24
No.
You can save yourself some calculation by learning a few of the basic Pythagorean triples, such as
3-4-5, 5-12-13, 8-15-17, 7-24-25
and their multiples.
This one is just 2 times 7,10,12 which is not one of the basics
To determine if a set of numbers represents a Pythagorean triple, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
So, let's check if the set of numbers 14, 20, and 24 satisfies the Pythagorean theorem.
Step 1: Arrange the numbers in ascending order.
14, 20, 24
Step 2: Determine the squares of the lengths of each side.
14^2 = 196
20^2 = 400
24^2 = 576
Step 3: Check if the sum of the squares of the two shorter sides is equal to the square of the longest side.
196 + 400 = 596
The sum of the squares of the two shorter sides is not equal to the square of the longest side (24^2 = 576), so the set of numbers 14, 20, and 24 does not represent a Pythagorean triple.