Help with a geometry challenge question. Need help asap, please!

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4boysmeme

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Dec 6, 2011
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Find the exact value(don't round) of DE, given AD = 12 and BD = 4.



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I don't even know how to start this problem. I am totally lost. Please solve step by step and explain to me. I will be tested on this later and I have to learn how to do it. thanks!!
 
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You don't get to do this. If you are totally lost and your exam is soon, you are toast. Neither we, nor anyone else, can work enough examples with you doing nothing to help you with your exam. You must learn the material and practice solving such problems.

If you truly have no clue, you MUST run to your academic advisor and have a VERY honest chat. We have to get you into a different class before you drown and learn to hate mathematics.
 
Hint: Look at the big right triangle. You know the lengths of both legs.

The smaller triangles within the big triangle are all similar to the big triangle. Therefore, the ratios of the sides are the same.
 
That was all that I was able to figure out on my on. Can you get me started on the next step, please.
 
Ok, this is what I came up with. CD = the square root of 48, CB=8, CE = 6 and the answer to the question (the exact value of DE) = the square root of 12.

Please tell me if this is correct.
 
You still have not shown us any work, so I cannot know where your mistakes are. Please show us your work.

Remember, two things must always be true: 1) these are all right triangles, so the Pythagorean Theorem must always be true, and 2) these triangles are all similar.

Additionally, you will find it *very* helpful to make your drawing as close to accurate in scale as possible. It doesn't have to be perfect by any means. This will help you visualize relative leg lengths for all your triangles and will give you a "quick check" on your results.

error: I applied given lengths to wrong segments, due to transposing pts C and D. Sorry for any confusion.

4boysmeme, I noticed you edited today. Did you switch points C and D without mentioning this fact???
 
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As already pointed out to you, all of the triangles defined in the figure are similar to one another. In addition, the starting triangle as well as the smaller triangles are all right triangles.

Perhaps you may not have heard of the fact that

1)the altitude to the hypotenuse of a right triangle is the geometric mean between the segments of the hypotenuse created by the point where the altitude intersects the hypotenuse or h^2 = xy. and

2)With an altitude drawn to the hypotenuse of a right triangle, each leg is the geometric mean between the hypotenuse and the segment of the hypotenuse in contact with the leg.


In this case, (CD)^2 = (AD)^2 (DB)^2 = 12(4) = 48 making DB = 4sqrt3.

Can you now see the door opening up to the derivation of DE, knowing CD and DB?

Give it a try. I know you can do it.
 
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