The area of trapezoid ABCD is 60. One base is 4 units longer than the other, and the height of the trapezoid is 5. Find the length of the median of the

The area of trapezoid ABCD is 60. One base is 4 units longer than the other, and the height of the trapezoid is 5. Find the length of the median of the trapezoid.

Let the parallel sides be  x and x+4

The area of a trapezium is  the average or the parallel sides multiplied by the height

\(Area=\frac{(x+x+4)}{2}*h\\~\\ Area=\frac{(2x+4)}{2}*5\\~\\ Area=\frac{2(x+2)}{2}*5\\~\\ Area=5(x+2)\\ 60=5(x+2)\\ 12=x+2\\ x=10 \)

The parallel sides are 10 and 14 units

Now the median length is the average of the paralel side lengths

Length of median = (10+14)/2 = 12 units

We have :

60  = 5/2 * ( x  +   x + 4)     where x is the length of the shorter base

60 (2/5)  = 2x + 4

24  = 2x + 4     subtract 4 from both sides

20  = 2x     divide both sides by 2

x = 10      and the longer base = 14

The  median  is  just  the average of the bases =    [10 +  14 ] / 2   =   24/2    = 12   units

I am curious Chris, when I started answering this question there was no indication that you were already answering.

I do not know what time that was.

When you started answering, did you see me?  I suppose I had not logged in so it doesn't mean much.  I do not think I have ever seen a note saying that a guest is answering.  Maybe guests cannot see that anyone is already answering either???

I would like to ask you this question again when I am logged in properly. I want to know how it works. :/

If I had known you were already answering I would have moved on to another question...........

No........when I answered this, there was no indication that anyone else was answering at the same time.....   Then.....I saw your answer..........weird......!!!!!!