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ASAPT

  • one year ago

Find the value of x and the value of y.

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  1. ASAPT
    • one year ago
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  2. ASAPT
    • one year ago
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    im not sure im pretty bad at geometry

  3. ASAPT
    • one year ago
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    ok do you know the answer?

  4. ASAPT
    • one year ago
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  5. anonymous
    • one year ago
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    You can't use the law of cosines unless you know the angle opposite the side you're looking for.

  6. ASAPT
    • one year ago
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    oh ok do you know the answer?

  7. ASAPT
    • one year ago
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    ugh why is this so difficult

  8. ybarrap
    • one year ago
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    Look at the lengths of CB and BA. What is their sum?

  9. ybarrap
    • one year ago
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    Compare this sum to 48. How is this possible?

  10. ybarrap
    • one year ago
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    There is only one explanation. Once you see this, the answer will POP.

  11. ybarrap
    • one year ago
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    Actually, just look at the lengths of CE and BA.

  12. ybarrap
    • one year ago
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    Sum them and compare to 48. What MUST x be in this case?

  13. ASAPT
    • one year ago
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    48?

  14. ybarrap
    • one year ago
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    You know that the lengths of 2 sides of a triangle MUST be greater than the third side, right?

  15. ASAPT
    • one year ago
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    yea

  16. ASAPT
    • one year ago
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    so what would that mean my answer is @ybarrap

  17. ybarrap
    • one year ago
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    forget about that approach

  18. ASAPT
    • one year ago
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    ok

  19. ASAPT
    • one year ago
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    its 12 12

  20. ybarrap
    • one year ago
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    this can't be right, forget that approach too. The reason is that y could be anything and that doesn't make sense.

  21. ASAPT
    • one year ago
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    no it was I submitted it and it said it was right

  22. ASAPT
    • one year ago
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    I have more to do if you want to help

  23. anonymous
    • one year ago
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    |dw:1436331441040:dw|

  24. ybarrap
    • one year ago
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    I just realized angle D and angle B are equal :( @surjithayer used similarity - Nice job!

  25. mathstudent55
    • one year ago
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    You are dealing with two similar triangles. Since <B =~ <CDE and <C =~ <C, by ASA Similarity, triangles ABC and EDC are similar. That makes the lengths of corresponding sides proportional. The easiest way to see this is to redraw the figure with the triangles separated and turned in the same direction so you can see the similarity. Se figure below. |dw:1436329185777:dw|

  26. mathstudent55
    • one year ago
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    Now we see how the triangles are similar. Since x is part of side BC, we need the length of side BC. From similarity, we get this proportion: \(\dfrac{CE}{CA} = \dfrac{CD}{BC} \) \(\dfrac{24}{48} = \dfrac{18}{BC} \) \(\dfrac{1}{2} = \dfrac{18}{BC} \) \(BC = 36\) Since \(BC = 36\), and \(CE = 24\), then \(x = BE = 36 - 24 = 12\) Now we need y. \(\dfrac{CE}{CA} = \dfrac{DE}{BA} \) \(\dfrac{24}{48} = \dfrac{y}{24} \) \(\dfrac{1}{2} = \dfrac{y}{24} \) \(y = 12\)

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