Question

1.

(Pythagorean Theorem LC)

Determine which set of side measurements could be used to form a triangle. (2 points)

15, 6, 21

14, 18, 5

7, 4, 2

6, 24, 14

Answer 1

Out of the sets of side measurements given, only the set (6, 24, 14) can form a triangle. This conclusion is based on the Pythagorean Theorem and the triangle inequality theorem. Therefore correct option is D

Step-by-step explanation:

Determining a Valid Triangle Using the Pythagorean Theorem

The Pythagorean Theorem relates the lengths of the sides of a right triangle and states that for a right triangle, the square of the length of the hypotenuse (c) is equal to the sum of the squares of the other two sides (referred to as legs a and b).

Using the formula a² + b² = c², we can determine if a set of three side lengths could form a right triangle. For any triangle, the sum of the lengths of any two sides must be greater than the length of the remaining side to form a valid triangle.

Let's evaluate the given sets of side measurements:

1. 15, 6, 21: 15² + 6² = 225 + 36 = 261 which is not equal to 21² (441), so these do not form a triangle.
2. 14, 18, 5: 14² + 5² = 196 + 25 = 221 which is less than 18² (324). This violates the triangle inequality theorem and therefore cannot form a triangle.
3. 7, 4, 2: 7 + 4 is less than 2 and also 7² + 4² is not equal to 2²; this cannot form a triangle.
4. 6, 24, 14: 6² + 14² = 36 + 196 = 232 which is less than 24² (576); these lengths can form a triangle.

The only set of side measurements that could be used to form a triangle is 6, 24, 14.