Is 9, 12, 15 the lengths of the sides of a right triangle? (show work)

Hello There!

To find out if these lengths make a triangle, you have to add up any two sizes and they must be greater than the third side for it to form a triangle.

Let's Test It!

"9+12=21" 21 is greater than 15

"9+15=24" 24 is greater than 12

Yes This Does Form A Triangle!

Yes, the triangle lengths 9, 12, and 15 are lengths of the sides of a right triangle.

Step-by-step explanation:

There are multiple different ways to prove that this answer is correct.

To begin, we could recognize that these side lengths are a Pythagorean triple, or multiples of side lengths that satisfy the Pythagorean theorem, and thus prove that the lengths constitute a right triangle. In this case, 9, 12, and 15 represent the 3, 4, 5 Pythagorean triple where each side length is multiplied by a factor of three.

3x3=9

4x3=12

5x3=15

Therefore, these side lengths do make a right triangle because they represent a multiple of a Pythagorean triple.

If we didn’t recognize this, we could always plug the side lengths into the Pythagorean theorem, a^2 + b^2 = c^2.

In this case, we get

9^2 + 12*2 = 15^2

If we simplify, we get:

81+144 = 225

And if simplified further, we get:

225=225,

Which is a true statement, proving that these side lengths do make up a right triangle.

Hope this helps!

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