Question

If the sides of the triangle are 12, 35, and 37, determine whether the triangle is a right-angled triangle. Justify.

A. Yes, by the Pythagorean theorem
B. No, the sides do not form a triangle
C. Yes, by the Law of Cosines
D. Cannot be determined with the given information

Answer 1

The given triangle with side lengths of 12, 35, and 37 is a right-angled triangle, determined by applying the Pythagorean theorem

Step-by-step explanation:

The given triangle has sides of lengths 12, 35, and 37. To determine whether the triangle is a right-angled triangle, we can use the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

By applying the Pythagorean theorem, we can check if it holds true for the given triangle:
12² + 35² = 37²
144 + 1225 = 1369
1369 = 1369

Since the equation holds true, we can conclude that the given triangle with side lengths of 12, 35, and 37 is a right-angled triangle. Therefore, the correct answer is A. Yes, by the Pythagorean theorem.