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anonymous

  • one year ago

Help please.... =*( If square ABCD has area 25, and the shape of the longer shaded square is 9 times the area of the smaller shaded square, what is the length of one side of the smaller shaded square?

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  1. anonymous
    • one year ago
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    |dw:1441124255042:dw|

  2. Michele_Laino
    • one year ago
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    we can write this: \[\Large {A_2} = 9{A_1} \Rightarrow L_2^2 = 9L_1^2 \Rightarrow {L_2} = 3{L_1}\] |dw:1441124497875:dw|

  3. anonymous
    • one year ago
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    whoa....

  4. anonymous
    • one year ago
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    can u make this a bit easier ?

  5. Michele_Laino
    • one year ago
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    furthermore, we have: \[\Large AB = {L_2} + {L_1} = 3{L_1} + {L_1} = 4{L_1}\]

  6. Michele_Laino
    • one year ago
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    finally, from your data, we have: \[\Large 5 = AB = 4{L_1}\]

  7. anonymous
    • one year ago
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    .....

  8. Michele_Laino
    • one year ago
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    please solve this equation for L1: \[\Large 5 = 4{L_1}\]

  9. Michele_Laino
    • one year ago
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    with A2 and A1 I meant the area of the largest shaded square and the area of the smallest shaded square respectively

  10. anonymous
    • one year ago
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    wow..... i really dont understand your explanation.

  11. anonymous
    • one year ago
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    |dw:1441125356826:dw|

  12. Michele_Laino
    • one year ago
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    from the text of your problem I read: "the shape of the longer shaded square is 9 times the area of the smaller shaded square" that statement is modeled by this equation: \[\Large {A_2} = 9{A_1}\] where with A2 and A1 are the area of the largest shaded square and the area of the smallest shaded square respectively

  13. Michele_Laino
    • one year ago
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    please refer to my drawings above

  14. Michele_Laino
    • one year ago
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    now, we can write this: \[\Large {A_2} = L_2^2\] and: \[\Large {A_1} = L_1^2\]

  15. anonymous
    • one year ago
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    nevermind u make things too complicated

  16. anonymous
    • one year ago
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    @Nnesha

  17. misty1212
    • one year ago
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    HI!!

  18. anonymous
    • one year ago
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    save me Misty

  19. misty1212
    • one year ago
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    lol this looks confusing but it can't be too bad can it?

  20. anonymous
    • one year ago
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    yea it's confusing... I've made no progress..

  21. misty1212
    • one year ago
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    the area of the big square is 25 right?

  22. anonymous
    • one year ago
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    yea so the length of one side is 5

  23. misty1212
    • one year ago
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    ok so the only thing i don't get is what "long shaded square" means is that the big square ?

  24. anonymous
    • one year ago
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    the bigger square inside the square yes

  25. anonymous
    • one year ago
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    i thought it would be |dw:1441127490171:dw|

  26. anonymous
    • one year ago
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    so |dw:1441127538111:dw|

  27. misty1212
    • one year ago
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    hold on is that the equation you derived?

  28. anonymous
    • one year ago
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    No i got that from the problem it says the longer shaded is 9 times the area of the smaller shaded

  29. misty1212
    • one year ago
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    cause it aint what i get

  30. anonymous
    • one year ago
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    what u get?

  31. misty1212
    • one year ago
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    |dw:1441127697875:dw|

  32. misty1212
    • one year ago
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    we know two things one is that \(x+y=5\) because the length is 5 the other is that \(x^2=9y^2\)

  33. misty1212
    • one year ago
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    so far so good?

  34. anonymous
    • one year ago
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    y is it 9y instead of 9x? i thought they said the longer shaded is 9 times the area of the smaller shaded?

  35. misty1212
    • one year ago
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    oh yeah you are right\[9x^2=y^2\]

  36. misty1212
    • one year ago
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    since \(x+y=5\) we know \(y=5-x\)

  37. misty1212
    • one year ago
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    so the equation to solve is \[9x^2=(5-x)^2\]

  38. anonymous
    • one year ago
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    ohhhhhhhhhhhhhhhhhhhhhhhh you just made me understand with the 9x^2 = y^2

  39. misty1212
    • one year ago
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    ok good! multiply out, put on one side of the equal sign, get \[8 x^2+10 x-25 = 0\]

  40. anonymous
    • one year ago
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    |dw:1441127982300:dw|