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=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)

Answer 1

To determine whether 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, which states that if \( a^2 + b^2 = c^2 \), then the triangle is a right triangle.

Let's calculate:

\( a^2 + b^2 = 3^2 + 4^2 = 9 + 16 = 25 \)

Now, let's calculate \( c^2 \):

\( c^2 = 5^2 = 25 \)

Since \( a^2 + b^2 = c^2 \) (25 = 25), this means that a right triangle can indeed be formed.

Thus, the answer is Option A: Yes, a right triangle can be formed.

So the answer is **1**.