To determine if the lengths 14, 50, and 48 satisfy the Pythagorean Theorem, we first identify the longest side, which we will consider as the hypotenuse. In this case, that side is 50. The Pythagorean Theorem states that in a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b).
The equation is:
\[ c^2 = a^2 + b^2 \]
Assign the sides as follows:
- \( a = 14 \)
- \( b = 48 \)
- \( c = 50 \)
Now we calculate:
- \( c^2 = 50^2 = 2500 \)
- \( a^2 + b^2 = 14^2 + 48^2 = 196 + 2304 = 2500 \)
Now we check if \( c^2 = a^2 + b^2 \):
\[ 2500 = 2500 \]
Since the equation holds true, the lengths do satisfy the Pythagorean Theorem.
So the answer is:
A. yes