Question

which of the following are right triangles: a triangle with side lenghts 6 inches, 8 inches,10 inches, a triangle with side lengths 8, 15, 17, a triangle with side lengths 5, 12, 13, a triangle with side lenght 4, 5, 6

Answer 1

9514 1404 393

Answer:

• (6, 8, 10) right
• (8, 15, 17) right
• (5, 12, 13) right

Step-by-step explanation:

It can be helpful to memorize a few of the Pythagorean triples that show up in Algebra problems. Their multiples also form right triangles.

  (3, 4, 5), (5, 12, 13), (7, 24, 25), (8, 15, 17), (9, 40, 41)

The triple (6, 8, 10) is the first one of these, multiplied by 2 inches.

The only triple that is a sequence of consecutive integers is (3, 4, 5), so you know immediately that (4, 5, 6) does not form a right triangle.

Of course, you can check any of them to see if the squares of the smaller two numbers total the square of the larger number:

  4² +5² = 16 +25 = 41 ≠ 6² . . . . . (4, 5, 6) is not a right triangle