Measure of Medians

[rubyred]

Question: If the Measure of the median of an isoscleles trapezoid is 5.5 what are the possible integral measures for the bases?


I don't know I have no idea how to set it up or solve for this equation, if their asking what the other 2 bases but they don't give me any other numbers to work with. I guessed From similiar problems I have done, and am wondering if it's right?

1. For the biggest base I would take 5.5-5.5=0 then i would add 0 + 5.5= _5.5___so that would be b1

2. For the smaller base 5.5-5.5=__0_ 5.5-0= ___5.5_

B1= 5.5
B2 = 5.5
Median=5.5

Please help ASAP Thanks

 

[Loren]

Have you looked up the definition of the median of a trapezoid? If so, you should realize that you add the two bases together and divide by 2 to get 5.5. That means you can add the two bases and get 11. The two bases don't have to be equal. I can see that there are several possibilities. Just remember that the bases are integers.

 

[Mrspi]

Question: If the Measure of the median of an isoscleles trapezoid is 5.5 what are the possible integral measures for the bases?


I don't know I have no idea how to set it up or solve for this equation, if their asking what the other 2 bases but they don't give me any other numbers to work with. I guessed From similiar problems I have done, and am wondering if it's right?

1. For the biggest base I would take 5.5-5.5=0 then i would add 0 + 5.5= _5.5___so that would be b1

2. For the smaller base 5.5-5.5=__0_ 5.5-0= ___5.5_

B1= 5.5
B2 = 5.5
Median=5.5

Please help ASAP Thanks

The median in a trapezoid joins the midpoints of the legs (the opposite non-parallel sides).

You should have a theorem which says The median in a trapezoid is parallel to the two bases, and its length is half the sum of the bases.

Suppose we let m = length of the median, and let b[sub:1t6vv06f]1[/sub:1t6vv06f] and b[sub:1t6vv06f]2[/sub:1t6vv06f] be the length of the two bases.

The above-mentioned theorem tells us that

m = (1/2)*(b[sub:1t6vv06f]1[/sub:1t6vv06f] + b[sub:1t6vv06f]2[/sub:1t6vv06f])

If m = 5.5, then

5.5 = (1/2)*(b[sub:1t6vv06f]1[/sub:1t6vv06f] + b[sub:1t6vv06f]2[/sub:1t6vv06f])

Multiply both sides by 2:

2*5.5 = 2*(1/2)*(b[sub:1t6vv06f]1[/sub:1t6vv06f] + b[sub:1t6vv06f]2[/sub:1t6vv06f])

11 = b[sub:1t6vv06f]1[/sub:1t6vv06f] + b[sub:1t6vv06f]2[/sub:1t6vv06f]

Now...you are asked for the possible INTEGRAL (they must be integers!) values for b[sub:1t6vv06f]1[/sub:1t6vv06f] and b[sub:1t6vv06f]2[/sub:1t6vv06f]. The length of a segment must be greater than 0, so you're limited to positive integers.

See what you can do with this information.....