Use the Converse of the Pythagorean Theorem to determine whether a right triangle can be formed given sides a

To determine whether a right triangle can be formed with the given sides \( a = 3 \), \( b = 5 \), and \( c = 6 \), we can use the Converse of the Pythagorean Theorem, which states that if \( a^2 + b^2 = c^2 \), then a right triangle can be formed with sides \( a \), \( b \), and \( c \).

Let's calculate \( a^2 \), \( b^2 \), and \( c^2 \):

\[ a^2 = 3^2 = 9 \] \[ b^2 = 5^2 = 25 \] \[ c^2 = 6^2 = 36 \]

Now, check if \( a^2 + b^2 = c^2 \):

\[ 9 + 25 = 34 \]

Since \( 34 \neq 36 \), \( a^2 + b^2 \) does not equal \( c^2 \).

So, based on the calculation:

No, a right triangle cannot be formed because \( 3^2 + 5^2 \neq 6^2 \).

Thus, the best response is:

No, a right triangle cannot be formed because 3 squared plus 5 squared is not equal to 6 squared.