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Joshuam1

  • 2 years ago

Triangle UVW is the pre-image of triangle RST with a scale factor of 3. Find the area of triangle UVW if the area of triangle RST is 9 cm2. 81 cm2 27 cm2 18 cm2 9 cm2

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  1. Joshuam1
    • 2 years ago
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    the triangle

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  2. srossd
    • 2 years ago
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    An intuitive way to think about this is that area is the square of distance. So, when you scale the distances of the sides by 3, the area scales by 9. So, 9 cm2 becomes 81 cm2.

  3. Joshuam1
    • 2 years ago
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    wow that was simple O_O

  4. Joshuam1
    • 2 years ago
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    I have some similar questions. Think you can have a look?

  5. srossd
    • 2 years ago
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    Absolutely

  6. Joshuam1
    • 2 years ago
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    Quadrilateral HIJK is the pre-image of quadrilateral LMNO. Find the scale factor, t.

  7. Joshuam1
    • 2 years ago
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  8. Joshuam1
    • 2 years ago
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    the options are 9/4 , 5/3, 9/25, 3/2

  9. srossd
    • 2 years ago
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    So, 375/135 = 2.77ish. You know from the last question that that's the square of the scale factor. Square root it and you get 1.66ish. So, 5/3.

  10. Joshuam1
    • 2 years ago
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    okay i have another I'm just working out what you said so i can have it for myself

  11. srossd
    • 2 years ago
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    Okay, let me know if you have any questions.

  12. Joshuam1
    • 2 years ago
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    Find WZ if the area of trapezoid ABCD is 225 cm2, the area of trapezoid WXYZ is 81 cm2, and AD is 35 cm.

  13. Joshuam1
    • 2 years ago
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    21 cm 12.6 cm 58.3 cm 97.2 cm

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  14. srossd
    • 2 years ago
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    So, find the scale factor first, like I did in the last question.

  15. Joshuam1
    • 2 years ago
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    okay :D

  16. Joshuam1
    • 2 years ago
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    2.77

  17. srossd
    • 2 years ago
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    Not quite, you forgot to take the square root.

  18. Joshuam1
    • 2 years ago
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    find the sqrt of 2.77?

  19. srossd
    • 2 years ago
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    Right, 225/81=2.77, but that's the ratio of the areas. To turn that into the ratio of lengths, you need the square root.

  20. Joshuam1
    • 2 years ago
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    the sqrt is 1.66

  21. srossd
    • 2 years ago
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    Right, so now use that to find WZ.

  22. Joshuam1
    • 2 years ago
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    how?

  23. srossd
    • 2 years ago
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    AB/WZ = 1.66

  24. Joshuam1
    • 2 years ago
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    35/21 =1.66

  25. srossd
    • 2 years ago
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    Right, so WZ = 21. Good job!

  26. Joshuam1
    • 2 years ago
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    :D sweet 2 more questions

  27. Joshuam1
    • 2 years ago
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    Find the area of the pre-image rectangle QRST if the area of the image rectangle DEFG is 54 cm^2 and the scale factor is 3/2

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  28. Joshuam1
    • 2 years ago
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    216 cm^2 108 cm^2 54 cm^2 24 cm^2

  29. srossd
    • 2 years ago
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    Well, with those choices, it's pretty obvious. It has to be less than 54. But still, try and work it out.

  30. Joshuam1
    • 2 years ago
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    okay :D what is the first step?

  31. srossd
    • 2 years ago
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    Square the scale factor,s ince you're working with area.

  32. Joshuam1
    • 2 years ago
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    2.25

  33. srossd
    • 2 years ago
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    Right. Now, you're going from post image to pre-image, so you have to divide by that.

  34. Joshuam1
    • 2 years ago
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    oh okay

  35. Joshuam1
    • 2 years ago
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    so square 54?

  36. Joshuam1
    • 2 years ago
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    2916

  37. Joshuam1
    • 2 years ago
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    wait oops my mistake

  38. srossd
    • 2 years ago
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    Are you doing 54/2.25?

  39. Joshuam1
    • 2 years ago
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    sorry no i divded 54 and 3/2

  40. srossd
    • 2 years ago
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    You need to divide by the squared ratio, since you're dealing with area.

  41. Joshuam1
    • 2 years ago
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    alright i got 24

  42. srossd
    • 2 years ago
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    Yup, nice job

  43. Joshuam1
    • 2 years ago
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    ty for all your help I am done :D

  44. srossd
    • 2 years ago
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    Great, no problem

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