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.
To determinewhether a right triangle can be formed using the given side lengths, we can use the Converse of the Pythagorean Theorem, which states that if the square of the length of the longest side is equal to the sum of the squares of the other two sides, then a right triangle can be formed.
In this case, let's calculate the squares of the side lengths:
a^2 = 16^2 = 256
b^2 = 12^2 = 144
c^2 = 20^2 = 400
According to the theorem, if a^2 + b^2 = c^2, then a right triangle can be formed. Let's check if the equation holds true:
256 + 144 = 400
Since the sum of the squares of the two shorter sides is equal to the square of the longest side, a right triangle can be formed.
Therefore, the answer is Option A: Yes, a right triangle can be formed.