Question

The side lengths of all of the shapes below are shown in inches. Select all the quadrilaterals with side lengths of 3, 6, 7, and 8 inches.

4
6
8
7

3
6
8
7

7
3
8
6

7
8
3
6

Answer 1

To determine which sets of side lengths can form a quadrilateral, we can use the triangle inequality principle, which states that the sum of the lengths of any three sides must be greater than the length of the fourth side.

Let's check each set of side lengths:

1. **Set 1: 4, 6, 8, 7**
- 4 + 6 + 7 > 8 → 17 > 8 (True)
- 4 + 6 + 8 > 7 → 18 > 7 (True)
- 4 + 7 + 8 > 6 → 19 > 6 (True)
- 6 + 7 + 8 > 4 → 21 > 4 (True)
- **Valid quadrilateral**

2. **Set 2: 3, 6, 8, 7**
- 3 + 6 + 7 > 8 → 16 > 8 (True)
- 3 + 6 + 8 > 7 → 17 > 7 (True)
- 3 + 7 + 8 > 6 → 18 > 6 (True)
- 6 + 7 + 8 > 3 → 21 > 3 (True)
- **Valid quadrilateral**

3. **Set 3: 7, 3, 8, 6**
- 7 + 3 + 6 > 8 → 16 > 8 (True)
- 7 + 3 + 8 > 6 → 18 > 6 (True)
- 7 + 6 + 8 > 3 → 21 > 3 (True)
- 3 + 6 + 8 > 7 → 17 > 7 (True)
- **Valid quadrilateral**

4. **Set 4: 7, 8, 3, 6**
- 7 + 8 + 6 > 3 → 21 > 3 (True)
- 7 + 8 + 3 > 6 → 18 > 6 (True)
- 7 + 6 + 3 > 8 → 16 > 8 (True)
- 8 + 6 + 3 > 7 → 17 > 7 (True)
- **Valid quadrilateral**

Based on the analysis, **all four sets** of side lengths provided (including those with lengths 3, 6, 7, and 8 inches) can form a valid quadrilateral.