Question

Which collection of three side lengths will not form a triangle

6, 10 18
10, 12 ,15
10, 15, 6
10, 18 ,12 please tell me how you figured it out.

Answer 1

To determine if a collection of three side lengths will form a triangle, we use the triangle inequality theorem. This theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. By applying this theorem to each collection of side lengths given, we can determine which ones will form a triangle.

Step-by-step explanation:

A triangle is a three-sided figure lying on a plane with three angles adding up to 180 degrees. To determine if a collection of three side lengths will form a triangle, we 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.

1. For the collection 6, 10, 18, the sum of the two smaller sides (6 + 10) is less than the largest side (18), so this collection will not form a triangle.
2. For the collection 10, 12, 15, the sum of the two smaller sides (10 + 12) is greater than the largest side (15), so this collection will form a triangle.
3. For the collection 10, 15, 6, the sum of the two smaller sides (6 + 10) is greater than the largest side (15), so this collection will form a triangle.
4. For the collection 10, 18, 12, the sum of the two smaller sides (10 + 12) is greater than the largest side (18), so this collection will form a triangle.

Answer 2

To construct a triangle, the sum of any 2 sides of the triangle should be greater than the third side of the triangle.
lets calculate the sums of all the given choices to find out which three lengths given do not form a triangle.

A.
6,10,18
6 + 10 = 16
16 is smaller than the third side-18
Therefore these 3 lengths do not form a triangle

B.10,12,15
10 + 12 = 22 15+12 = 27 15 + 10 = 25
22>15 (3rd side) 27>10 (3rd side) 25>12 (3rd side)
In this triangle, sum of all the possible pairs of sides are greater than the third side therefore these lengths can form a triangle

C.10,15,6
10 + 15 = 25 15 + 6 = 21 10+6 = 16
25 > 6 21>10 16>15
in this too, sum of all the possible pairs of sides are greater than the third side. These lengths can be used to form a triangle

D.10,18 ,12
10 + 18 = 28 18 + 12 = 30 10 +12 = 22
28> 12 30>10 22> 18
Therefore these lengths can also be used to form a triangle

correct answer is 6,10 and 18 these cannot form a triangle