Are the following numbers a Pythagorean Triple? 10, 24, 23 (you must show your work and explain, if they are or are not a Pythagorean triple)
My question:
Are the following numbers a Pythagorean Triple? 9, 21, 25 (you must show your work and explain, if they are or are not a Pythagorean triple)
Answer: If the 3 numbers form a Pythagorean triple, then the largest must be the hypotenuse
and 9^2 + 21^2 = 25^2
Is that true?
9^2 + 21^2
= 81 + 441 = 522
and 25^2 = 625 , so I guess they don't form a Pythagorean triple.
Convert my solution to your problem.
@Reiny Thank you so much!
you're a LIFE SAVER!!!! thanks reiny
To determine whether a set of three numbers forms a Pythagorean triple, we can use the Pythagorean theorem. According to the theorem, in a right-angled 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 two other sides.
In this case, the numbers given are 10, 24, and 23. Let's check if they satisfy the Pythagorean theorem:
Step 1: Square the values for each number.
10^2 = 100
24^2 = 576
23^2 = 529
Step 2: Check if the sum of the squares of the smaller sides equals the square of the largest side.
100 + 576 = 676
Step 3: Compare the result from step 2 to the square of the largest side.
676 = 23^2
Since the sum of the squares of the two smaller sides (100 + 576) equals the square of the largest side (676), the numbers 10, 24, and 23 form a Pythagorean triple.
Therefore, the answer is yes, the numbers 10, 24, and 23 form a Pythagorean triple.