Question

If the mid segment of a trapezoid measures 6 units long, what is true about the lengths of the bases of the trapezoid?

Answer 1

C'mon now, this is exactly what we just did..... Tell me about it.

Answer 2

Really? Gosh.

Answer 3

But isn't it asking for properties and such?

Answer 4

I can find it, but the question is unclear to me.

Answer 5

Didn't we just work two problems based on the idea that the length of the mid segment of a trapezoid is the average of the two bases?

Answer 6

x+2x/2=6?

Answer 7

Not always. Your equation is valid for the case when the larger base is twice the smaller. In that case, (x+2x)/2=6. In general, \[\frac{b_1+b_2}{2}=6\]

Answer 8

Of course, since the bases are line segments, their lengths have to be more than zero.

Answer 9

So x+2x/2=6? won't work all the time?

Answer 10

When finding the lengths not including the mid segment?

Answer 11

Look, a trapezoid might be almost a rectangle, with the two bases just about identical, or it could be just about a triangle with the top cut off, so the two bases are a lot different. The important thing in this problem is that they average to six units long.

Answer 12

I don't think you will get a specific number for this problem. You could state it with one base in terms of the other, like \[b_2=12-b_1~~~b_1\in (0,12)\]Another way to say\[b_1\in (0,12)~is~0<b_1<12\]

Answer 13

Answer: The sum of the lengths of the two bases is 12.