Question

Check if the following triangles are right triangles, whose sides have the following measures:

1. Triangle with side lengths 6, 10, and 8.
A) Yes, it's a right triangle.
B) No, it's not a right triangle.

2. Triangle with side lengths 50, 120, and 13.
A) Yes, it's a right triangle.
B) No, it's not a right triangle.

3.Triangle with side lengths 11, 9, and 2.
A) Yes, it's a right triangle.
B) No, it's not a right triangle.

Answer 1

Using the Pythagorean theorem to check if triangles are right angles, it has been determined that the triangle with sides 6, 10, and 8 is a right triangle, while the triangles with sides 50, 120, and 13, and 11, 9, and 2 are not.

Step-by-step explanation:

To determine whether the given triangles are right triangles, we can use the Pythagorean theorem, which states that for a right 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. This can be expressed as a² + b² = c², where a and b are the sides and c is the hypotenuse.

1. For the triangle with side lengths 6, 10, and 8, we apply the theorem and calculate 6² + 8² = 36 + 64 = 100, which is equal to 10². Therefore, this is a right triangle.
2. For the triangle with side lengths 50, 120, and 13, we calculate 50² + 13² = 2500 + 169 = 2669, which is not equal to 120² (14400). So, this is not a right triangle.
3. Lastly, for the triangle with side lengths 11, 9, and 2, we calculate 11² + 2² = 121 + 4 = 125, which is not equal to 9² (81). This is not a right triangle either.

The answers are: 1. A) Yes, it's a right triangle. 2. B) No, it's not a right triangle. 3. B) No, it's not a right triangle.