Final answer:
There are three different sized rectangles that can be made using 14 toothpicks: 1x6, 2x5, and 3x4, considering that each rectangle is counted only once regardless of orientation.
Step-by-step explanation:
To determine how many different sized rectangles can be made using 14 toothpicks, we need to think about the perimeter of a rectangle, which is the total length of its sides.
A rectangle has two lengths (L) and two widths (W), and the perimeter (P) can be calculated using the formula P = 2L + 2W.
With 14 toothpicks, the formula becomes 14 = 2L + 2W.
If we divide through by 2, we get 7 = L + W.
The possible integer combinations for L and W that satisfy this equation are limited, but they include (1,6), (2,5), (3,4), and the reverse of each (6,1), (5,2), (4,3).
However, we count each rectangle only once regardless of orientation, so there are three different sized rectangles that can be made with 14 toothpicks: 1x6, 2x5, and 3x4.