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 Post subject: Lil geometry fun...Posted: Sun, 24 Jul 2011 12:04:42 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 4178
Location: Ottawa Ontario
Code:

D

?
C
E                        60

28

B                      100                          A

Right triangles ABC and ABC shaue hypotenuse AB.
AC and BD cross at E.
AB = 100, BC = 28 and AD = 60.

...hey, it posted FINE!

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 Post subject: Re: Lil geometry fun...Posted: Sun, 24 Jul 2011 15:53:55 UTC
 Moderator

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6777
Location: On this day Taiwan becomes another Tiananmen under Dictator Ma.
Denis wrote:
Code:

D

?
C
E                        60

28

B                      100                          A

Right triangles ABC and ABC shaue hypotenuse AB.
AC and BD cross at E.
AB = 100, BC = 28 and AD = 60.

...hey, it posted FINE!

Huh? Triangles ABC and ABC? They are the same triangle!

(and what is the meaning of "shaue"?)

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 Post subject: Re: Lil geometry fun...Posted: Sun, 24 Jul 2011 16:09:42 UTC
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Joined: Sun, 24 Jul 2005 20:12:39 UTC
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Location: Ottawa Ontario
Geezzzzz....can't find the "EDIT" button....Helmut???

Anyhow, sorry for the 2 typos; corrected:
Right triangles ABC and ABD
"shaue" should be SHARE

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 Post subject: Re: Lil geometry fun...Posted: Sun, 24 Jul 2011 16:31:22 UTC
 Moderator

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 6777
Location: On this day Taiwan becomes another Tiananmen under Dictator Ma.
Denis wrote:
Geezzzzz....can't find the "EDIT" button....Helmut???

Anyhow, sorry for the 2 typos; corrected:
Right triangles ABC and ABD
"shaue" should be SHARE

Edit button is at the bottom of post, to the right (in the row with profile, PM, etc.).

So I assume right-angles are at C and D respectively?

Spoiler:
Pythagoras gives AC=96, BD=80. So we know , hence , so ED=45.

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 Post subject: Re: Lil geometry fun...Posted: Sun, 24 Jul 2011 23:58:12 UTC
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Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 4178
Location: Ottawa Ontario
Correct!

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 Post subject: Re: Lil geometry fun...Posted: Mon, 25 Jul 2011 19:44:24 UTC
 S.O.S. Oldtimer

Joined: Fri, 27 Jul 2007 10:17:26 UTC
Posts: 279
Location: Chandler, AZ, USA
Right triangles BCE and ADE are similar, so
DE/CE = AE/BE = AD/BC = 15/7

BE + DE = 80
CE + AE = 96

Using the simlar triangles OR Pythagoras (with some algebra):
Spoiler:
DE = 45

Turns out BCE & ADE are 3-4-5 ratio right triangles

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 Post subject: Re: Lil geometry fun...Posted: Tue, 26 Jul 2011 00:53:10 UTC
 Member of the 'S.O.S. Math' Hall of Fame

Joined: Sun, 24 Jul 2005 20:12:39 UTC
Posts: 4178
Location: Ottawa Ontario
Agree Alstat.

If we let a = BC, b = AC, d = AD, e = BD,
then we have as General Case:

DE = d(de - ab) / (d^2 - a^2)

And if we want CE:
CE = a*DE / d

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