Pythagorean Theorem Proofs Quick Check

Question

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Question
Using the Converse of the Pythagorean Theorem, explain whether a triangle with sides 15, 10, and 12 is a right triangle.(1 point)
Responses

No, because 325 is not equal to 144.
No, because 325 is not equal to 144.

No, because 369 is not equal to 100.
No, because 369 is not equal to 100.

No, because 22 is not equal to 15.
No, because 22 is not equal to 15.

No, because 244 is not equal to 225.
No, because 244 is not equal to 225.
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Answer 1

To determine if a triangle with sides 15, 10, and 12 is a right triangle using the Converse of the Pythagorean Theorem, you need to check whether the square of the longest side is equal to the sum of the squares of the other two sides.

1. Identify the longest side. Here, the longest side is 15.

2. Calculate the squares:

   • \(15^2 = 225\)
   • \(10^2 = 100\)
   • \(12^2 = 144\)

3. Now, check if \(15^2\) is equal to \(10^2 + 12^2\): \[ 225 \stackrel{?}{=} 100 + 144 \] \[ 225 = 244 \quad (\text{False}) \]

Since \(225 \neq 244\), this means the triangle does not satisfy the Pythagorean theorem condition for a right triangle.

The correct response based on the provided options would be:

No, because 244 is not equal to 225.