Which of the following measurements, in centimeters, could be the lengths of the sides of a triangle? Select all that apply.
a)3cm,4cm,5cm
b)4cm,10cm,14cm
c)5cm,11cm,15cm
d)6cm,6cm,13cm
e)7cm,4cm,12cm
f)8cm,10cm,17cm
THANK YOU!
Pythagorean theorem. A squared plus B squared equals C squared. Answer A is always a triangle. None of the rest can form triangles.
I think it is a
To determine if the given measurements could be the lengths of the sides of a triangle, we need to check if they satisfy the triangle inequality theorem. According to this theorem, in a triangle, the sum of the lengths of any two sides must be greater than the length of the third side.
Let's check each option:
a) 3cm, 4cm, 5cm
4 + 5 > 3 (True)
3 + 4 > 5 (True)
3 + 5 > 4 (True)
Based on the triangle inequality theorem, option a) is valid.
b) 4cm, 10cm, 14cm
4 + 10 > 14 (False)
4 + 14 > 10 (True)
10 + 14 > 4 (True)
The lengths in option b) do not satisfy the triangle inequality theorem.
c) 5cm, 11, 15cm
5 + 11 > 15 (False)
5 + 15 > 11 (True)
11 + 15 > 5 (True)
The lengths in option c) do not satisfy the triangle inequality theorem.
d) 6cm, 6cm, 13cm
6 + 6 > 13 (False)
6 + 13 > 6 (True)
6 + 13 > 6 (True)
The lengths in option d) do not satisfy the triangle inequality theorem.
e) 7cm, 4cm, 12cm
4 + 7 > 12 (False)
4 + 12 > 7 (True)
7 + 12 > 4 (True)
The lengths in option e) do not satisfy the triangle inequality theorem.
f) 8cm, 10cm, 17cm
8 + 10 > 17 (False)
8 + 17 > 10 (True)
10 + 17 > 8 (True)
The lengths in option f) do not satisfy the triangle inequality theorem.
Therefore, the valid options are a) 3cm, 4cm, 5cm.
To determine if a set of measurements could be the lengths of the sides of a triangle, we can use the Triangle Inequality Theorem. According to this theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
Let's go through each option:
a) 3cm, 4cm, 5cm
To check if this forms a triangle:
3 + 4 > 5 (True)
4 + 5 > 3 (True)
5 + 3 > 4 (True)
Since all three inequalities hold true, this set of measurements could be the lengths of the sides of a triangle.
b) 4cm, 10cm, 14cm
To check if this forms a triangle:
4 + 10 > 14 (False)
10 + 14 > 4 (True)
14 + 4 > 10 (True)
Since one of the inequalities does not hold true (4 + 10 ≤ 14), this set of measurements cannot be the lengths of the sides of a triangle.
c) 5cm, 11cm, 15cm
To check if this forms a triangle:
5 + 11 > 15 (True)
11 + 15 > 5 (True)
15 + 5 > 11 (True)
Since all three inequalities hold true, this set of measurements could be the lengths of the sides of a triangle.
d) 6cm, 6cm, 13cm
To check if this forms a triangle:
6 + 6 > 13 (False)
6 + 13 > 6 (True)
13 + 6 > 6 (True)
Since one of the inequalities does not hold true (6 + 6 ≤ 13), this set of measurements cannot be the lengths of the sides of a triangle.
e) 7cm, 4cm, 12cm
To check if this forms a triangle:
7 + 4 > 12 (False)
4 + 12 > 7 (True)
12 + 7 > 4 (True)
Since one of the inequalities does not hold true (7 + 4 ≤ 12), this set of measurements cannot be the lengths of the sides of a triangle.
f) 8cm, 10cm, 17cm
To check if this forms a triangle:
8 + 10 > 17 (False)
10 + 17 > 8 (True)
17 + 8 > 10 (True)
Since one of the inequalities does not hold true (8 + 10 ≤ 17), this set of measurements cannot be the lengths of the sides of a triangle.
Based on the analysis, the measurements that could be the lengths of the sides of a triangle are:
a) 3cm, 4cm, 5cm
c) 5cm, 11cm, 15cm