Which of the following sets of numbers could not represent the three sides of a triangle?
Answers
Answer:
Options A, D
Step-by-step explanation:
The way that we will be checking if these 3 numbers can represent a triangle is by checking if a + b ≥ c. That means that the first two sides have to be greater than or equal to the third side.
Step 1: Determine if Option A is a triangle
10 + 16 = 26 <- 26 is less than 27 that means that it cannot form a triangle.
Step 2: Determine if Option B is a triangle
14 + 28 = 42 <- 42 is greater than 39 which means that these three numbers can form a triangle.
Step 3: Determine if Option C is a triangle
12 + 27 = 39 <- 39 is equal to 39 which means that these three numbers can form a right triangle.
Step 4: Determine if Option D is a triangle
8 + 22 = 30 <- 30 is less than 31 meaning that these three numbers can't form a triangle.
Answer: Options A, D
Final answer:
To determine if a set of numbers can represent the sides of a triangle, we need to check if the sum of the lengths of any two sides is greater than the length of the third side. Two sets of numbers that could not represent the sides of a triangle are 1, 2, 3 and 4, 5, 9.
Explanation:
In order for three numbers to represent the sides of a triangle, the sum of the lengths of any two sides must be greater than the length of the third side, which is known as triangle inequality. Let's consider the options:
- 1, 2, 3: The sum of the lengths of the two smaller sides is 1+2=3, which is equal to the length of the longest side. This does not satisfy the triangle inequality, so this set of numbers could not represent the sides of a triangle.
- 4, 5, 9: The sum of the lengths of the two smaller sides is 4+5=9, which is equal to the length of the longest side. This does not satisfy the triangle inequality, so this set of numbers could not represent the sides of a triangle.
- 6, 8, 10: The sum of the lengths of the two smaller sides is 6+8=14, which is greater than the length of the longest side (10). This satisfies the triangle inequality, so this set of numbers could represent the sides of a triangle.
Therefore, the sets of numbers that could not represent the sides of a triangle are 1, 2, 3 and 4, 5, 9.
Learn more about Triangle Inequality here:
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Is it math? what kind of subject is it? i can help you :)