so if a trapezoid has 4 sides and the top(short) side and the two not parallel sides are all 5 inches long, what are possible lengths for the long (bottom) side? and are there more than 1 possible solution?
To determine the possible lengths for the long (bottom) side of a trapezoid with known side lengths, we need to consider the properties of a trapezoid.
A trapezoid has two parallel sides, called bases, and two non-parallel sides, called legs. In this case, the top side is one of the bases and the two non-parallel sides have lengths of 5 inches each.
Since the top side is shorter than the bottom side, we need to find a range of possible lengths for the bottom side. To do this, we can use the Triangle Inequality theorem, which states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
In this context, we can treat the trapezoid as a degenerate triangle (a triangle with one side of length 0) by visualizing the top side extending to the bottom side.
Based on the given information, the top side has a length of 5 inches and both non-parallel sides also have lengths of 5 inches. Therefore, we can apply the Triangle Inequality theorem:
5 + 5 > x, where x is the length of the bottom side.
Simplifying the equation, we have:
10 > x
This inequality tells us that any length (x) of the bottom side must be less than 10 inches to satisfy the Triangle Inequality theorem.
To find the highest possible length of the bottom side, we can use the fact that the length of the bottom side is greater than or equal to the length of the top side. Thus, the maximum possible length of the bottom side is 5 inches.
To summarize, the possible lengths for the long (bottom) side of this trapezoid are any value less than 10 inches and greater than or equal to 5 inches. There is only one possible solution, as the length of the bottom side cannot be greater than 5 inches based on the given information.