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**thedarktiger****Member**- Registered: 2014-01-10
- Posts: 83

In pentagon ABCDE, BC=CD=DE=2 units, <E is a right angle and m<B = m<C = m<D = 135 degrees. The length of segment AE can be expressed in simplest radical form as a+2sqrt(b) units. What is the value of a+b?

This is actually a lot of 45 45 90 triangles!

a+2*sqrt(b)

A xxxxxxxxxxxxxxxxxxxxxx E

x x

x x 2

x x D

n x 2 x x

x x x sqrt(2)

B xxxxxxxxxxxxxxx

C sqrt(2)

2

Then I drew BE and got that BE = sqrt(2(2+sqrt(2))^2)=sqrt(2)*(2+sqrt(2))

Then <ABE is 45 so ABE is 45 45 90 so AB = BE so AE = sqrt(2*(sqrt(2)*(2+sqrt(2)))^2) = 4*(2+sqrt(2)) = 8 + 4*sqrt(2) = 8 + 2*sqrt(8)

so the answers 8+8=16

whats wrong I got it wrong:(:D

Good. You can read.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,528

hi thedarktiger

Hopefully the right diagram below.

I agree with everything up to the last calculation but simplify BE

Bob

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

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**thedarktiger****Member**- Registered: 2014-01-10
- Posts: 83

nice! thats correct! I wish the thing I'm doing had solutions

Good. You can read.

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,528

hi

Is this from "Compuhigh" ?

Bob

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

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**phrontister****Real Member**- From: The Land of Tomorrow
- Registered: 2009-07-12
- Posts: 3,915

Hi,

This is what I did:

Triangles ABG and EBG are congruent, from which...

AE = 2GE = 2BF = 2(2+√2) = 4+2√2.

The length of segment AE can be expressed in simplest radical form as a+2√b units.

a = 2BC = 2x2 = 4, and b = CD = 2......from which CF = √2 (Pythagoras) and hence CF also = √b.

∴ a+b = 4+2 = 6

Proof:

AE = a+2√b = 4+2√2.

The first image is with Geogebra and the second is with Word. I was just fiddling around, comparing ease of use, speed, accuracy, presentation etc. Because I use Word a fair bit it didn't take all that long there, but with Geogebra it took about 1/2 Word's time...once I'd worked out some moves.

*Last edited by phrontister (2014-01-14 19:28:50)*

"The good news about computers is that they do what you tell them to do. The bad news is that they do what you tell them to do." - Ted Nelson

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