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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=3 , b=4 , and c=5 . 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).

1 answer

To determine whether a right triangle can be formed using the sides a = 3, b = 4, and c = 5, we apply the Converse of the Pythagorean Theorem, which states that if the square of the length of the longest side (c) is equal to the sum of the squares of the other two sides (a and b), then a right triangle can be formed.

Let's calculate:

  1. \( c^2 = 5^2 = 25 \)
  2. \( a^2 + b^2 = 3^2 + 4^2 = 9 + 16 = 25 \)

Since \( c^2 = a^2 + b^2 \), we find:

\( 25 = 25 \)

This means that a right triangle can indeed be formed.

So the answer is:

Option A: Yes, a right triangle can be formed. (1)