Answer :
Final answer:
To determine if a triangle is right, use the Pythagorean theorem to check if the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides. Triangle a is not right, triangle b is not right, and triangle c is not right.
Explanation:
To determine whether a triangle is a right triangle, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides. Let's check each triangle:
a. The lengths of the sides are 4, 28, and y. Using the Pythagorean theorem, we have 4^2 + 28^2 = y^2. Solving this equation, we find that y = 28.7. Therefore, this triangle is not a right triangle.
b. The lengths of the sides are 195, y, and 197. Using the Pythagorean theorem, we have 195^2 + y^2 = 197^2. Solving this equation, we find that y = 18. Therefore, this triangle is not a right triangle.
c. The lengths of the sides are 197, y, and y. Using the Pythagorean theorem, we have 197^2 = 2y^2. Solving this equation, we find that y = 98.5. Therefore, this triangle is not a right triangle.
