Use the Pythagorean Theorem Practice

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Question
A triangle has sides a
, b
, and c
. Use the Converse of the Pythagorean Theorem to determine whether a right triangle can be formed if a=16
, b=12
, and c=20
.

Option A: Yes, a right triangle can be formed.

Option B: No, a right triangle cannot be formed.

Choose 1 for Option A or 2 for Option B.

(1 point)

Answer 1

To determine whether a triangle with sides \( a = 16 \), \( b = 12 \), and \( c = 20 \) can be a right triangle, we can use the Converse of the Pythagorean Theorem. The theorem states that if \( c \) is the longest side of a triangle, then the triangle is a right triangle if and only if \( a^2 + b^2 = c^2 \).

Let's calculate:

1. \( a^2 = 16^2 = 256 \)
2. \( b^2 = 12^2 = 144 \)
3. \( c^2 = 20^2 = 400 \)

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

\[ 256 + 144 = 400 \]

Since \( 400 = 400 \), the equation holds true.

Therefore, the answer is:

Option A: Yes, a right triangle can be formed.