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**harrychess****Member**- Registered: 2014-04-04
- Posts: 34

Please Help! I need someone to explain how to work this problem.

The diagonals of a trapezoid are perpendicular and have lengths 8 and 10. Find the length of the median of the trapezoid.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 87,164

Hi

I am getting

**In mathematics, you don't understand things. You just get used to them.Of course that result can be rigorously obtained, but who cares?Combinatorics is Algebra and Algebra is Combinatorics.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,418

hi harrychess,

By using Sketchpad and measuring, I'm getting this:

AC = 10, BD = 8. AB parallel to DB.

I can move E about, and still get the same result for FG, which is interesting as the whole shape changes.

Using those right angled triangles, it's not too hard to show that the area of ABCD = 0.5 x 8 x 10.

So if I could calculate h, the height of the trapezium, then the length of FG would be easy.

But I cannot see how to get h just yet. Still thinking ....................................

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,418

Ok. Extra bits on diagram:

h = HD = CI. The angles marked with a dot are equal (alternate angles). Say, alpha.

So using the area I have already worked out and

where a and b are the lengths of the parallels, you can work out FG.

Bob

*Last edited by bob bundy (2014-07-31 00:49:14)*

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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