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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.

Mellie  Dec 12, 2015

Best Answer 

 #2
avatar+90988 
+15

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

Melody  Dec 12, 2015
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4+0 Answers

 #1
avatar+78577 
+15

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

 

 

 

cool cool cool

CPhill  Dec 12, 2015
 #2
avatar+90988 
+15
Best Answer

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

Melody  Dec 12, 2015
 #3
avatar+90988 
+5

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...........

Melody  Dec 12, 2015
 #4
avatar+78577 
+5

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

 

 

 

 

cool cool cool

CPhill  Dec 12, 2015

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