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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

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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

#2
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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.

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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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

CPhill  Dec 12, 2015
#2
+94105
+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
#3
+94105
+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. :/

Melody  Dec 12, 2015
#4
+92669
+5

CPhill  Dec 12, 2015