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

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 325 is not equal to 144.

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 first need to identify the longest side, which is 15 in this case.

According to the Pythagorean Theorem, for a triangle with sides \( a \), \( b \), and \( c \) (where \( c \) is the longest side), it is a right triangle if \( a^2 + b^2 = c^2 \).

Let's assign the sides:
- \( a = 10 \)
- \( b = 12 \)
- \( c = 15 \)

Now calculate \( a^2 + b^2 \) and \( c^2 \):
- \( a^2 + b^2 = 10^2 + 12^2 = 100 + 144 = 244 \)
- \( c^2 = 15^2 = 225 \)

Now, compare \( a^2 + b^2 \) to \( c^2 \):
- \( 244 \) is not equal to \( 225 \).

Since \( a^2 + b^2 \neq c^2 \), we conclude that the triangle with sides 15, 10, and 12 is **not a right triangle**.

Thus, the correct response is:
**No, because 244 is not equal to 225.**