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 if a right triangle can be formed using the sides \(a = 3\), \(b = 4\), and \(c = 5\), we can use the Converse of the Pythagorean Theorem. According to this theorem, if the square of the length of the longest side (hypotenuse) is equal to the sum of the squares of the other two sides, then a right triangle can be formed.

Let's check:

  1. Identify the longest side: Here, \(c = 5\) is the longest side.

  2. Calculate the squares:

    • \(a^2 = 3^2 = 9\)
    • \(b^2 = 4^2 = 16\)
    • \(c^2 = 5^2 = 25\)
  3. Check the equation:

    • \(c^2 = a^2 + b^2\)
    • \(25 = 9 + 16\)
    • \(25 = 25\) (True)

Since the equation holds true, a right triangle can indeed be formed with these side lengths.

Thus, the answer is:

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

Choose 1 for Option A.