Question

Which set of integers is not a Pythagorean triple?


A.
9, 40, 41







B.
11, 60, 61







C.
15, 18, 21







D.
20, 21, 29

Answer 1

Are you familiar with the Pythagorean Theorem?

Answer 2

No

Answer 3

The should have a ratio of 3:4:5

Answer 4

This is the part of it that is needed here.

Here is a right triangle.
The two sides that form the right angle have lengths a and b. They are called the legs.
The side opposite the right angle has length c. It is called the hypotenuse.

Answer 5

In a right triangle, this equation is always true:

\(a^2 + b^2 = c^2\)

where a and b are the lengths of the legs, and c is the length of the hypotenuse.

Answer 6

That equation is what we get from the Pythagorean Theorem.

Answer 7

So how do I use that with this equation?

Answer 8

The hypotenuse is always the longest side in a right triangle.
That means the hypotenuse is always represented by c.

Answer 9

For each group of three numbers, replace c with the largest number, and a and b with the other two, in either order.
If the equation is true, it is a Pythagorean triple, and the triangle with those side lengths is a right triangle.

Answer 10

Let's do the first choice as an example together.
The numbers are 9, 40, 41
41 is the largest number, so we put in for c.
9 and 40 are used for a and b in either order.

\(a^2 + b^2 = c^2 \)

First, we just substitute the numbers in for a, b, and c.

\(9^2 + 40^2 = 41^2\)

Answer 11

Now we see if these three numbers make the equation true.

81 + 1600 = 1681

1681 = 1681

Since the equation is true (because 1681 really is equal to 1681), this is a Pythagorean triple.

Now you can move on to the next choice.