6

enter image description here

AE=7.2 cm,AD=7.6 cm,BE=4.2 cm and BC=8.4 cm.

Now,find DE.

So,if we apply Pythagoras theorem in AED we have $ED=\sqrt {7.6^2-7.2^2}=2.433$.

But,if we apply similarity between AED and ACB, we have $\frac {AD}{DE}=\frac {AB}{BC}$ and thus solving we get DE=5.6 cm.

So,why this inconsistency in results?

Soham
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    You should consider the possibility that the given figure is impossible. –  Sep 18 '16 at 15:30
  • so what do you want to calculate? – Dr. Sonnhard Graubner Sep 18 '16 at 15:30
  • @Dr.SonnhardGraubner I want to calculate $DE$... – Soham Sep 18 '16 at 15:36
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    @tatan Suppose you have $AE$, $EB$ and $BC$. From those values you can completely determine $AD$, but you'll get a different value than $7.6$. Hence your figure is impossible. – Anon Sep 18 '16 at 15:38
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    This is a perfectly reasonable question that shows effort -- I don't understand the downvote. – mweiss Sep 18 '16 at 16:01
  • @McFry Your comment should be posted as an answer. – mweiss Sep 18 '16 at 16:06
  • @mweiss how you say it is reasonable question? – Sathasivam K Sep 18 '16 at 16:10
  • Before doing problems if you check whether you write the correct question in your paper,you won't lead to such a misleading. Then how you say its reasonable @mweiss. – Sathasivam K Sep 18 '16 at 16:16
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    The OP is considering a question and has found, by two different methods, two different solutions. He or she wants to know how to reconcile or otherwise account for those two contradictory results. The resolution is that the initial figure is impossible -- but that is hardly self-evident (and in fact the OP's dilemma is itself a proof of that figure). Seems like a very good question to me. – mweiss Sep 18 '16 at 16:20

3 Answers3

4

As McFry has said in the comments, the figure is impossible. Suppose we try to construct it. First, we construct right triangle $AED$ with the indicated measurements,and extend segment $AE$ so that $EB$ is $4.2$ units long, as shown:

enter image description here

Now to finish the construction we extend $AD$ and drop a perpendicular from $B$ to $AD$, as shown:

enter image description here

Note that the length of $BC$ is completely determined by the construction so far. In fact, one can determine using similarity that $BC \approx 3.65$. So there is no way to satisfy the conditions of the given diagram, which requires $BC = 8.4$.

mweiss
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If you draw a circle with $AB$ as diameter on x axis, and midpoint of $AB$ as origin, let $A$ be negative and $B$ be positive, then $C$ will lie in first quadrant with given $AC$ length and in second quadrant with given $CB$ length. Since $C$ is a right angle, $C$ has to lie on the circle. Hence the construction is not possible.

jnyan
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Your drawing is misleading, try making a figure to scale.

enter image description here

Michael Biro
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