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#1 2007-06-05 19:20:03

Identity
Member
Registered: 2007-04-18
Posts: 934

Rectangle Measurements

This is a problem that I've had a bit of a headache over, find the length FG.
If possible, please only use similarity, congruency, pythagoras, and trigonometry, to do this, not coordinate geometry or anything too advanced. Thanks!

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#2 2007-06-05 23:28:18

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Rectangle Measurements

I think this way works.

We can tell length BE by Pythagoras, because we know AB and AE. So BE = √(6²+4.5²) = 7.5.
We know EF (by Pythagoras and also because it's given), so taking that away gives that BF = 5.

Triangles ABG and CFG are similar, because they can be shown to have two matching angles, and we also know that each side of ABG is 1.5 times as big as those of CFG.

BF = BG+FG, and because those two triangles are similar that means that BF = 2.5FG.
Therefore, 2.5FG = 5 --> FG = 2cm.


Why did the vector cross the road?
It wanted to be normal.

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#3 2007-06-06 00:10:11

Identity
Member
Registered: 2007-04-18
Posts: 934

Re: Rectangle Measurements

How are FGC and BGC similar? Could you please provide a proof?

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#4 2007-06-06 03:00:09

mathsyperson
Moderator
Registered: 2005-06-22
Posts: 4,900

Re: Rectangle Measurements

I never said they were, I said that ABG and CFG were similar. You get ABG by enlarging CFG by a scale factor of -1.5, with the point of enlargement at G.

You can show this by the X and Z rules of parallel lines.


Why did the vector cross the road?
It wanted to be normal.

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#5 2007-06-06 10:32:17

Identity
Member
Registered: 2007-04-18
Posts: 934

Re: Rectangle Measurements

Thanks mathsy!

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