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 244 is not equal to 225. No, because 244 is not equal to 225. No, because 22 is not equal to 15.

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 first identify the longest side, which is 15. We will then check if the square of the longest side is equal to the sum of the squares of the other two sides.

1. Square the lengths of the sides:

   • Longest side: \(15^2 = 225\)
   • Other sides:
     • \(10^2 = 100\)
     • \(12^2 = 144\)

2. Sum the squares of the shorter sides:

   • \(10^2 + 12^2 = 100 + 144 = 244\)

3. Compare the squares:

   • The square of the longest side is \(225\).
   • The sum of the squares of the other two sides is \(244\).

Since \(225\) is not equal to \(244\), we conclude that the triangle is not a right triangle.

From the provided options, the correct response is: No, because 244 is not equal to 225.