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**+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

#1**+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**+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**+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