Question

Use the Converse of the Pythagorean Theorem to determine whether a right triangle can be formed given sides a
, b
, and c
, where a=3
, b=5
, and c=6
.(1 point)
Responses

No, a right triangle cannot be formed because 32+52≠62
.
No, a right triangle cannot be formed because 3 squared plus 5 squared is not equal to 6 squared .

Yes, a right triangle can be formed because the Pythagorean Theorem produced a false statement.
Yes, a right triangle can be formed because the Pythagorean Theorem produced a false statement.

No, a right triangle cannot be formed because 32+52=62
.
No, a right triangle cannot be formed because 3 squared plus 5 squared equals 6 squared .

Yes, a right triangle can be formed because 32+52=62
.

Answer 1

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.**