+0

# 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

0
646
4
+1760

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
+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
Sort:

#1
+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

CPhill  Dec 12, 2015
#2
+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
#3
+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. :/

Melody  Dec 12, 2015
#4
+78577
+5

CPhill  Dec 12, 2015

### 10 Online Users

We use cookies to personalise content and ads, to provide social media features and to analyse our traffic. We also share information about your use of our site with our social media, advertising and analytics partners.  See details