SOLUTION: Can the converse of the Pythagorean theorem determine which triangle with the given three side lengths is a right triangle. 16,21,24 4,9,12 20,21,29 5,12,14

Algebra.Com
Question 1182225: Can the converse of the Pythagorean theorem determine which triangle with the given three side lengths is a right triangle.
16,21,24
4,9,12
20,21,29
5,12,14
Found 2 solutions by mananth, Edwin McCravy:
Answer by mananth(16946)   (Show Source): You can put this solution on YOUR website!

16,21,24
choose the longest side. If it is a right triangle then 24 will be the hypotenuse.
Let's try
24 ^2 = 576 ----------(1)
16^2+21^ = 697----------(2)
(1) not equal to (2)
so it is not a right triangle
If they are equal then it is a right triangle



Answer by Edwin McCravy(20055)   (Show Source): You can put this solution on YOUR website!
16,21,24.
  
162 + 212 = 242
256 + 441 = 576
      697 = 576
       Nope!
4,9,12
42 + 92 = 122
16 + 81 = 144
     97 = 144
       Nope!
20,21,29
202 + 212 = 292
400 + 441 = 841
      841 = 841
       Yep!
5,12,14
52 + 122 = 142
25 + 144 = 196
     169 = 196
       Nope!

Edwin
RELATED QUESTIONS

use the fact that the converse of the Pythagorean Theorem is a true statement to... (answered by vleith)
The converse of the Pythagorean theorem is also a true statement: If the sum of the... (answered by Edwin McCravy)
How can I know whether a triangle is acute, obtuse, or right, based on three side... (answered by bucky)
How do I Determine which of the following side lengths for triangle ABC would form a... (answered by ikleyn)
A right triangle has side lengths that are consecutive even integers. Use the... (answered by whisper)
what is the equation? use Pythagorean theorem to find the length of the hypotenuse of a... (answered by nyc_function)
If triangle ABC is a triangle such that a^2 + b^2 = c^2, then angle BCA is a right... (answered by jojo14344)
The lengths of three sides of a right triangle are consecutive even integers. Find the... (answered by edjones)
Pythagorean theorem The longer leg of a right triangle is 3m longer than the shorter... (answered by Fombitz)