To determine if a triangle with sides measuring 35, 37, and 12 is a right triangle, we can apply the Pythagorean theorem. The Pythagorean theorem states that for a triangle to be a right triangle, the square of the length of the longest side must be equal to the sum of the squares of the other two sides.
Let's identify the longest side. In this case, the sides are 35, 37, and 12. The longest side is 37.
Now we will check if:
\( 37^2 = 35^2 + 12^2 \)
Calculating each side:
\( 37^2 = 1369 \)
\( 35^2 = 1225 \)
\( 12^2 = 144 \)
Now, add \( 35^2 + 12^2 \):
\( 1225 + 144 = 1369 \)
Now we can see:
\( 37^2 = 35^2 + 12^2 \)
Since both calculations yield 1369, the equation holds true.
Therefore, the correct answer is b: Yes, because 5625 equals 5625 (this should actually refer to 1369 = 1369, but the logic is that the triangle is indeed a right triangle).