Which set of numbers could not represent the lengths of the sides of a right triangles?

Question

A. {3, 4, 5}

B. {6, 9, 12}

C. {5, 12, 13}

D. {8, 15, 17}

Answer 1

Someday, probably very soon, math classes will begin to teach the use of computers (with spreadsheets and easy computer languages) soon after they allow/teach the use of calculators (for calculation, graphing, etc.).

It it time to learn about Pythagorean Triples (sets of three numbers that satisfy the Pythagorean Theorem). These appear in many, many math homework problems (because calculations use integers) and on many standardized tests (e.g., SAT and ACT). Not that (6,8,10), for example, is a multiple of (3,4,5).

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

(20, 21, 29) (12, 35, 37) (9, 40, 41) (28, 45, 53)

. . .

Answer 2

Because the triangle is a right triangle, you would make use of the Pythagorean Theorem : a² + b² = c² where 'c' is the longest side of the triangle and 'a' and 'b' are the remaining two sides.

To solve this problem, you would plug in the values into this equation to figure out if all these numbers allow the equation to work out.

For example, choice a provides the side lengths of 3, 4 and 5. In this case c = 5 and a = 3 and b = 4 (the assignments to 'a' and 'b' could also be reversed: a = 4 and b = 3).

So, plugging into the equation you get: 3² + 4² = 5². So now, we have to check if this is true.

This gives you 9 + 16 = 25. This is indeed true, which means that these sides for a right triangle.

If you continue this method for the rest of the choices, you'll realize that choice B: 6, 9, 12 would not work out.

In this case, c = 12 and a = 6 and b = 9.

So, plugging into the equation you get: 6² + 9² = 12². So now, we have to check if this is true.

This gives you 36 + 81 = 144. This is not true as 36+81 = 117 which does NOT equal 144. Therefore, these lengths of sides could NOT form a right triangle.

Answer 3

B. {6, 9, 12}