which of the following sets sides lengths can be used to draw a triangle ? Remember the Triangle Inequality Theorem
To determine if a set of side lengths can be used to draw a triangle, we need to apply the Triangle Inequality Theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's look at the sets of side lengths:
1) 3, 4, 7
To check if a triangle can be formed, we compare each pair of sides:
- 3 + 4 = 7 (greater than 7). This pair satisfies the Triangle Inequality Theorem.
- 3 + 7 = 10 (greater than 4). This pair satisfies the Triangle Inequality Theorem.
- 4 + 7 = 11 (greater than 3). This pair satisfies the Triangle Inequality Theorem.
Since all pairs satisfy the theorem, a triangle can be formed with side lengths 3, 4, and 7.
2) 5, 9, 15
To check if a triangle can be formed:
- 5 + 9 = 14 (less than 15). This pair does not satisfy the Triangle Inequality Theorem.
- 5 + 15 = 20 (greater than 9). This pair satisfies the Triangle Inequality Theorem.
- 9 + 15 = 24 (greater than 5). This pair satisfies the Triangle Inequality Theorem.
Not all pairs satisfy the theorem, so a triangle cannot be formed with side lengths 5, 9, and 15.
3) 2, 2, 6
To check if a triangle can be formed:
- 2 + 2 = 4 (less than 6). This pair does not satisfy the Triangle Inequality Theorem.
- 2 + 6 = 8 (greater than 2). This pair satisfies the Triangle Inequality Theorem.
- 2 + 6 = 8 (greater than 2). This pair satisfies the Triangle Inequality Theorem.
Not all pairs satisfy the theorem, so a triangle cannot be formed with side lengths 2, 2, and 6.
Therefore, the set of side lengths that can be used to draw a triangle is 3, 4, and 7.
wrong
I apologize for the mistake. Let's reevaluate the sets of side lengths:
1) 3, 4, 7
To check if a triangle can be formed, we compare each pair of sides:
- 3 + 4 = 7 (greater than 7). This pair satisfies the Triangle Inequality Theorem.
- 3 + 7 = 10 (greater than 4). This pair satisfies the Triangle Inequality Theorem.
- 4 + 7 = 11 (greater than 3). This pair satisfies the Triangle Inequality Theorem.
Since all pairs satisfy the theorem, a triangle can be formed with side lengths 3, 4, and 7.
2) 5, 9, 15
To check if a triangle can be formed:
- 5 + 9 = 14 (less than 15). This pair does not satisfy the Triangle Inequality Theorem.
- 5 + 15 = 20 (greater than 9). This pair satisfies the Triangle Inequality Theorem.
- 9 + 15 = 24 (greater than 5). This pair satisfies the Triangle Inequality Theorem.
Not all pairs satisfy the theorem, so a triangle cannot be formed with side lengths 5, 9, and 15.
3) 2, 2, 6
To check if a triangle can be formed:
- 2 + 2 = 4 (equal to 6). This pair does not satisfy the Triangle Inequality Theorem.
- 2 + 6 = 8 (greater than 2). This pair satisfies the Triangle Inequality Theorem.
- 2 + 6 = 8 (greater than 2). This pair satisfies the Triangle Inequality Theorem.
Not all pairs satisfy the theorem, so a triangle cannot be formed with side lengths 2, 2, and 6.
Therefore, the correct set of side lengths that can be used to draw a triangle is 3, 4, and 7.
wrong these are the answer choices
2 cm , 3 cm, 6 cm
6 cm, 5 cm 10 cm
7 cm, 9 cm, 16 cm
10 cm , 10 cm, 20 cm
Let's analyze each set of side lengths using the Triangle Inequality Theorem:
1) 2 cm, 3 cm, 6 cm
- 2 + 3 = 5 (less than 6). This pair does not satisfy the Triangle Inequality Theorem.
- 2 + 6 = 8 (greater than 3). This pair satisfies the Triangle Inequality Theorem.
- 3 + 6 = 9 (greater than 2). This pair satisfies the Triangle Inequality Theorem.
Not all pairs satisfy the theorem, so a triangle cannot be formed with side lengths 2 cm, 3 cm, and 6 cm.
2) 6 cm, 5 cm, 10 cm
- 6 + 5 = 11 (greater than 10). This pair satisfies the Triangle Inequality Theorem.
- 6 + 10 = 16 (greater than 5). This pair satisfies the Triangle Inequality Theorem.
- 5 + 10 = 15 (greater than 6). This pair satisfies the Triangle Inequality Theorem.
All pairs satisfy the theorem, so a triangle can be formed with side lengths 6 cm, 5 cm, and 10 cm.
3) 7 cm, 9 cm, 16 cm
- 7 + 9 = 16 (equal to 16). This pair does not satisfy the Triangle Inequality Theorem.
- 7 + 16 = 23 (greater than 9). This pair satisfies the Triangle Inequality Theorem.
- 9 + 16 = 25 (greater than 7). This pair satisfies the Triangle Inequality Theorem.
Not all pairs satisfy the theorem, so a triangle cannot be formed with side lengths 7 cm, 9 cm, and 16 cm.
4) 10 cm, 10 cm, 20 cm
- 10 + 10 = 20 (equal to 20). This pair does not satisfy the Triangle Inequality Theorem.
- 10 + 20 = 30 (greater than 10). This pair satisfies the Triangle Inequality Theorem.
- 10 + 20 = 30 (greater than 10). This pair satisfies the Triangle Inequality Theorem.
Not all pairs satisfy the theorem, so a triangle cannot be formed with side lengths 10 cm, 10 cm, and 20 cm.
Therefore, the only set of side lengths that can be used to draw a triangle is 6 cm, 5 cm, and 10 cm.