Answer:
A) 8.4
Explanation:
The given nine decimal numbers in order of size from the smallest to the largest are:
- 1.2, 2.2, 2.8, 3, 3.8, 4.2, 5, 5, 7
The numbers along each side of the provided triangle must add to 14.2 using four of the given decimal numbers, where the numbers placed at the vertices of the triangle are shared by two sides.
The combinations of four numbers from the list that add up to 14.2 are:
- 1.2 + 2.2 + 3.8 + 7 = 14.2
- 1.2 + 3 + 5 + 5 = 14.2
- 1.2 + 3.8 + 4.2 + 5 = 14.2
- 2.2 + 2.8 + 4.2 + 5 = 14.2
There is only one combination that involves 7. Therefore, we can place 7 on side AB.
This means that two of the three numbers remaining from this combination (1.2, 2.2 and 3.8) should be placed at vertices A and B. Since 1.2 appears in two further combinations, whereas 2.2 and 3.8 appear in one further combination, we should place 1.2 at vertex A. We cannot place 3.8 at vertex B since the only other combination that includes 3.8 also includes 1.2, so place 2.2 at vertex B and 3.8 in the remaining space on side AB.
Therefore, the remaining combinations are now:
- 1.2 + 3 + 5 + 5 = 14.2
- 1.2 + 3.8 + 4.2 + 5 = 14.2
- 2.2 + 2.8 + 4.2 + 5 = 14.2
Since vertex A is 1.2 and vertex B is 3.8, we can immediately discount the second of the three remaining combination as this sum is now impossible. Therefore, the remaining combinations for sides AC and BC are:
- 1.2 + 3 + 5 + 5 = 14.2
- 2.2 + 2.8 + 4.2 + 5 = 14.2
Both combinations include a 5, therefore place 5 at vertex C.
To complete the triangle, place 3 and 5 on side AC, and 2.8 and 4.2 on side BC.
The triangle is now complete, with all nine numbers placed to ensure that the numbers along each side sum to the required 14.2.
In summary:
- Vertex A = 1.2
- Vertex B = 2.2
- Vertex C = 5
Therefore, the sum of A, B and C is:
A + B + C = 1.2 + 2.2 + 5
A + B + C = 8.4