Math

The ramp shown below is used to move crates of apples to loading docks at different heights. When the horizontal distance AB is 12 feet, the height of the loading dock, BC, is 6 feet. What is the height of the loading dock DE?

10 feet
12 feet
17 feet***
18 feet
Ok so this is a test question and I missed this one but they let me redo it... and 17 feet is the right answer and I just have to show why but Idk why?

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  1. the question doesn't make sense unless you have a picture.

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  2. I know but it wouldn't let me post it and it told me to submit URL to Jiskha

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  3. Why don't you just describe the diagram?
    It looks like we can use a straight ratio for this.

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  4. Ok its a triangle and A-B is 12 feet and C-B is 6 feet and B-D is 22 feet and I have to figure out what the length is for D-E

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  5. We can figure out that AC is sqrt180 because it is sqrt(12^2+6^2)=sqrt(144+36) = sqrt180. Draw a line starting from point C parallel to line BD and ending at point F on line ED. This means that DF is also 6, and that CF is 22. Call the length of FE the letter x. That makes ED=x+6. The length of AE is AC+CE, and we know AC is sqrt180, so we need to find CE. CF is 22 and FE is x, so using the Pythagorean Theorum we have CE=sqrt(22^2+x^2)=sqrt(484+x^2). So AE=sqrt180+sqrt(484+x^2). Next we find AE in different terms, using the whole right triangle. AD=34 and DE is x+6, so AE is sqrt(34^2+(x+6)^2)=sqrt(1156+x^2+12x+36) =sqrt(x^2+12x+1192). Using the two equations for AE, we have sqrt180+sqrt(484+x^2)=sqrt(x^2+12x+1192). Simplifiying the equation, we get the quadratic formula 576x^2-12672x+69696=0, and solve to get x=11, and since DE is x+6, DE=11+6=17.

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  6. Or you could just use similar triangles and say that DE is x, so x/6=(12+22)/12, which simplifies to x/6=34/12 = x/6=17/6, so x=17

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  7. Ok I'm so so thankful for u helping me that is like Japanese to me. Im sorry

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  8. Ok im sorry I didn't see the last thing u posted but that makes a lot more sense thank you very very much! :D

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  9. You description is not good enough
    but I am going to guess that DE is the height.

    Not even going to read the reply directly above, looks way tooooo complicated

    by simple ratio:
    h/34 = 6/12
    12h = 204
    h = 204/12 =17

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  10. Ok but what is the h?

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  11. Ok I figured it out thank ya'll so much for your help! :)

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  12. It is 9 for 4 and ab 12 bc

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  13. this is so confusing haha
    thanks anyways

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