Question

Is a triangle with sides of the length of 6 ft, 21 ft, and 23 ft a right triangle?

Answer 1

All you have to do is the pythagorean theorem. 

6 squared + 21 squared = 23 squared

If this is true, then it is a right triangle.

 In this case, it isn't. It is not a right triangle.

Answer 2

To solve this problem, you can plug your values for the triangle's side lengths into the Pythagorean Theorem. The Pythagorean Theorem is a² + b² = c², where c is the hypotenuse of a right triangle. The hypotenuse is the longest side of the triangle, so when you plug in your values for this triangle, you must plug 23 for c, like so:

6² + 21² = 23²

Now you can solve; if 6² + 21² is indeed equal to 23², the triangle is a right triangle.

6² + 21² = 23²
36 + 441 = 529
477 ≠ 529

477 is not equal to 529, so this triangle is not a right triangle.