Use the Pythagorean Theorem Quick Check

Question

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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=6
, b=10
, and c=12
.(1 point)
Responses

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 62+102≠122
.
No, a right triangle cannot be formed because 6 squared plus 10 squared is not equal to 12 squared .

Yes, a right triangle can be formed because 62+102=122
.
Yes, a right triangle can be formed because 6 squared plus 10 squared equals 12 squared .

No, a right triangle cannot be formed because 62+102=122
.

Answer 1

To determine whether a right triangle can be formed with sides \(a = 6\), \(b = 10\), and \(c = 12\) using the Converse of the Pythagorean Theorem, we need to check if the following equation holds:

\[ a^2 + b^2 = c^2 \]

Substituting the values we have:

\[ 6^2 + 10^2 = 12^2 \]

Calculating each side:

\[ 36 + 100 = 144 \]

Now, we check \(c^2\):

\[ 12^2 = 144 \]

Since \(36 + 100 = 144\) is true, we can conclude:

\[ 6^2 + 10^2 = 12^2 \]

This indicates that a right triangle can indeed be formed with sides \(6\) and \(10\) as the legs and \(12\) as the hypotenuse.

Therefore, the correct response is:

Yes, a right triangle can be formed because \(6^2 + 10^2 = 12^2\).