SOLUTION: LM is the midsegment of trapezoid ABCD. AB=x+8, LM=4x+3, and DC=187. What is the value of x? Please explain not sure how to work this out.

Question 550573: LM is the midsegment of trapezoid ABCD. AB=x+8, LM=4x+3, and DC=187. What is the value of x? Please explain not sure how to work this out.
Found 2 solutions by mathstutor494, solver91311:
Answer by mathstutor494(120) (Show Source): You can put this solution on YOUR website!
Length of the midsegment of a trapezoid is the average length of the bases,
i.e. LM = (AB+DC)/2
Substituting the values given, we get
4x+3 = ((x+8)+187))/2
Multiplying both sides by 2 ...
> 2*(4x+3) = ((x+8)+187))
> 8x+6 = x+195
> 8x-x = 195-6
> 7x = 189
> x = 27 ( Dividing both sides by 7)

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!

The measure of the midsegment (the segment whose endpoints are the midpoints of the non-parallel sides of the trapezoid) of a trapezoid is the average of the measures of the two parallel sides.

The two parallel sides are and , so the average is which, according to the givens is:

And this average has to be equal to the given measure of the midsegment, so:

Solve for .

John

My calculator said it, I believe it, that settles it

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