Pythagorean Theorem Proofs Quick Check

Question

3 of 53 of 5 Items

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

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

No, because 244 is not equal to 225.

Answer 1

To determine if a triangle with sides 15, 10, and 12 is a right triangle using the Converse of the Pythagorean Theorem, we need to check if the squares of the lengths of the two shorter sides add up to the square of the length of the longest side.

1. Identify the sides:

   • The lengths are 15, 10, and 12.
   • Here, the longest side is 15.

2. Calculate the squares:

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

3. Check the Pythagorean Theorem:

   • According to the theorem, for a right triangle: \( (shorter\ side)^2 + (other\ shorter\ side)^2 = (longest\ side)^2 \)
   • For this triangle: \(10^2 + 12^2 = 100 + 144 = 244\)
   • Compare that to \(15^2 = 225\).

Since \(244\) is not equal to \(225\), this means that 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.