Question
\#2) Which of the following sets could NOT be the sides of a right triangle? * 1 point \( 1,2,3 \) \( 3,4,5 \) \( 5,12,13 \) \( 6,8,10 \)
Ask by Mckenzie Pritchard. in the United States
Feb 26,2025
Upstudy AI Solution
Tutor-Verified Answer
Answer
The set 1, 2, 3 cannot be the sides of a right triangle.
Solution
To determine which set of numbers cannot be the sides of a right triangle, we apply the Pythagorean theorem. This theorem states that in a right triangle, if the sides are a, b (legs) and c (the hypotenuse), then:
a² + b² = c²
Let's examine each option:
1. For the set 1, 2, 3, assume the largest number (3) is the hypotenuse:
1² + 2² = 1 + 4 = 5
3² = 9
Since 5 ≠ 9, these do not satisfy the Pythagorean theorem. Additionally, 1 + 2 = 3, which means the sides would form a degenerate triangle.
2. For the set 3, 4, 5:
3² + 4² = 9 + 16 = 25
5² = 25
These satisfy the theorem.
3. For the set 5, 12, 13:
5² + 12² = 25 + 144 = 169
13² = 169
These satisfy the theorem.
4. For the set 6, 8, 10:
6² + 8² = 36 + 64 = 100
10² = 100
These satisfy the theorem.
Thus, the set that could NOT be the sides of a right triangle is 1, 2, 3.
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Simplify this solution Mind Expander
To determine which set of sides could NOT form a right triangle, you can use the Pythagorean theorem, \( a^2 + b^2 = c^2 \), where \( c \) is the hypotenuse (the longest side). For \( 1, 2, 3 \): \( 1^2 + 2^2 = 1 + 4 = 5 \) (which does not equal \( 3^2 \)). So, this set cannot form a right triangle. However, the other sets—\( 3, 4, 5 \), \( 5, 12, 13 \), and \( 6, 8, 10 \)—do satisfy the theorem. So the answer is \( 1, 2, 3 \). This exercise showcases the beauty of geometry in analyzing relationships between sides! Who knew math could be so revealing?
