Question

Using the side lengths of the given triangles (not drawn to scale), determine which ones are right triangles?

1) Triangle A: sides 3, 4, 5
2) Triangle B: sides 6, 8, 10
3) Triangle C: sides 7, 24, 25
4) Triangle D: sides 9, 12, 15

Answer 1

By applying the Pythagorean theorem, it is determined that Triangles A (3, 4, 5), B (6, 8, 10), and C (7, 24, 25) are right triangles because they satisfy the condition a² + b² = c². Triangle D (9, 12, 15) does not satisfy this condition and is therefore not a right triangle.

Step-by-step explanation:

To determine which of the given triangles are right triangles, we can apply the Pythagorean theorem, which states that in 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 represented as a² + b² = c², where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.

Let's check each triangle:

1. Triangle A: 3² + 4² = 9 + 16 = 25, which matches 5². Therefore, Triangle A is a right triangle.
2. Triangle B: 6² + 8² = 36 + 64 = 100, which matches 10². Therefore, Triangle B is also a right triangle.
3. Triangle C: 7² + 24² = 49 + 576 = 625, which matches 25². Triangle C is a right triangle because these values satisfy the Pythagorean theorem.
4. Triangle D: 9² + 12² = 81 + 144 = 225, which does not match 15² (225). Therefore, Triangle D is not a right triangle.

Triangles A, B, and C are all right triangles based on the Pythagorean theorem.