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November 8th, 2018, 03:25 AM   #1
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what is the length

What is x in the attached? All I can think of is to draw a line from A to E, but that doesn't seem to help much either.

Answer is 2 * sqrt 6, but I do not know how they obtained this.
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Last edited by skipjack; November 8th, 2018 at 08:46 AM.
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November 8th, 2018, 05:45 AM   #2
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First off ABCD is a rectangle even if you choose not to draw it that way.

Second with the information show the problem is indeterminate as the following picture illustrates.

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November 8th, 2018, 06:45 AM   #3
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Quote:
Originally Posted by romsek View Post
First off ABCD is a rectangle even if you choose not to draw it that way.

Second with the information show the problem is indeterminate as the following picture illustrates.

Did you see that AB and BE are equal to each other? And how can you say ABCD is a rectangle? What makes you think the other two corners are right angles? I didn't catch that part.

Last edited by skipjack; November 8th, 2018 at 08:47 AM.
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November 8th, 2018, 06:58 AM   #4
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I disagree with the above. I doubt that it's intended that there are right angles at A and C, and even if there are, it doesn't seem to follow that ABCD is a rectangle.

Also, the rectangle diagrams don't support BA = BE.

However, a plausible diagram would be a good idea.
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November 8th, 2018, 07:12 AM   #5
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Quote:
Originally Posted by skipjack View Post
I disagree with the above. I doubt that it's intended that there are right angles at A and C, and even if there are, it doesn't seem to follow that ABCD is a rectangle.

Also, the rectangle diagrams don't support BA = BE.

However, a plausible diagram would be a good idea.
Is that what those squiggles mean?

Do you think the square at A and C means those two angles are equal?

Last edited by skipjack; November 8th, 2018 at 08:48 AM.
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November 8th, 2018, 07:55 AM   #6
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Is that what those squiggles mean?

Do you think the square at A and C means those two angles are equal?
Square at A and C means they are right angles.

Last edited by skipjack; November 8th, 2018 at 08:48 AM.
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November 8th, 2018, 08:04 AM   #7
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I think ketanco is mistaken. My analysis indicates that the angles at A and C are equal, but are not right angles. Also, a correct diagram is quite surprising and very different in appearance from the deliberately misdrawn diagram provided.

However, I've not yet found a proof that the diagram I have in mind is unique.
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November 8th, 2018, 08:20 AM   #8
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Connect B with D and let $\displaystyle BD=d$. Also, let $\displaystyle BA=BE=y$.

Then from right triangle $\displaystyle ABD$ we get $\displaystyle x^2=d^2-y^2$.

From right triangle $\displaystyle BDC$ we get $\displaystyle BC^2=d^2-7^2$.

From right triangle $\displaystyle BEC$ we get $\displaystyle BC^2=y^2-5^2$.

So, $\displaystyle d^2-49=y^2-25$ and $\displaystyle d^2-y^2=49-25=24$.

Thus, $\displaystyle x^2=24$ and $\displaystyle x=2 \sqrt{6}$.
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November 8th, 2018, 08:35 AM   #9
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Here is a picture.
pic1.jpg
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November 8th, 2018, 10:15 AM   #10
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Quote:
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Connect B with D and let $\displaystyle BD=d$. Also, let $\displaystyle BA=BE=y$.

Then from right triangle $\displaystyle ABD$ we get $\displaystyle x^2=d^2-y^2$.

From right triangle $\displaystyle BDC$ we get $\displaystyle BC^2=d^2-7^2$.

From right triangle $\displaystyle BEC$ we get $\displaystyle BC^2=y^2-5^2$.

So, $\displaystyle d^2-49=y^2-25$ and $\displaystyle d^2-y^2=49-25=24$.

Thus, $\displaystyle x^2=24$ and $\displaystyle x=2 \sqrt{6}$.
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