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

Answer 1

To determine whether the triangle with sides 15, 10, and 12 is a right triangle using the Converse of the Pythagorean Theorem, we can follow these steps:

1. Identify the longest side: In this case, the longest side is 15.

2. Use the Pythagorean Theorem: The Converse of the Pythagorean Theorem states that for a triangle with sides \(a\), \(b\), and \(c\) (where \(c\) is the longest side), if \(a^2 + b^2 = c^2\), then the triangle is a right triangle.

3. Calculate \(a^2 + b^2\) and \(c^2\):

   • Let \(a = 10\), \(b = 12\), and \(c = 15\).
   • Calculate \(a^2 + b^2\): \[ 10^2 + 12^2 = 100 + 144 = 244 \]
   • Calculate \(c^2\): \[ 15^2 = 225 \]

4. Compare the results:

   • We found that \(a^2 + b^2 = 244\) and \(c^2 = 225\).
   • Since \(244 \neq 225\), the triangle does not satisfy the condition for being a right triangle.

Therefore, the triangle with sides 15, 10, and 12 is not a right triangle. The correct response is: "No, because 244 is not equal to 225."