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missashleyn

Can someone help me, please? The sun roof in Troy’s house is shaped like a rectangle. He increases the length of the sides of the sun roof to five times the existing ones. How will this change affect the perimeter of the sun roof? It will be 20 times the original perimeter. It will be 5 times the original perimeter. It will be 10 times the original perimeter. It will be 15 times the original perimeter.

  • one year ago
  • one year ago

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  1. TajanaeXD
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    It depends on what the given perimeter is, my guess is that its 20

    • one year ago
  2. missashleyn
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    They didn't give me a perimeter :/

    • one year ago
  3. whpalmer4
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    We don't need to know the original perimeter.

    • one year ago
  4. missashleyn
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    Oh then I have absolutely no idea how to figure this out :(

    • one year ago
  5. TajanaeXD
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    Well in some cases there should be. But if there isn't the best answer on the top of my head is like 20

    • one year ago
  6. whpalmer4
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    Perimeter is just the sum of all of the sides. Let's make p be the original perimeter. Now he increases the sides to be 5 times the original ones. Well, for a rectangle, the perimeter is length + length + width + width, or 2*length + 2*width. Now we are making our perimeter be 5*length + 5*length + 5*width + 5*width = 10*length + 10*width. Compare the old perimeter (2*length + 2*width) with the new (10*length + 10*width). What is the ratio?

    • one year ago
  7. missashleyn
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    I am so confused, ratio of what?

    • one year ago
  8. whpalmer4
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    If you like, take a roof that is square, and 1 unit on each side. (squares are rectangles). Perimeter is 1+1+1+1 = 4. Okay, now make it a square 5 units on a side. Perimeter is 5+5+5+5 = 20. 20/4 = 5. So, multiplying the sides by 5 makes the perimeter also be multiplied by 5.

    • one year ago
  9. whpalmer4
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    The ratio of the new perimeter (bigger roof, with sides 5x as long) to the old perimeter (original roof).

    • one year ago
  10. missashleyn
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    So the perimeter will be 5 times the original perimeter?

    • one year ago
  11. whpalmer4
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    Yes!

    • one year ago
  12. TajanaeXD
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    Yep pretty much

    • one year ago
  13. missashleyn
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    Oh wow, that's confusing. I have another question like this.. could you help me with it too?

    • one year ago
  14. whpalmer4
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    Fire away, let's make it less confusing :-)

    • one year ago
  15. missashleyn
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    Lol okay! A museum exhibit, ABCD, has infrared beams around it for security, as shown. If the length of the beams is doubled on each side, which statement is correct about the maximum area available for an exhibit to be displayed? It becomes six times the original area. It becomes double the original area. It becomes four times the original area. It becomes eight times the original area.

    • one year ago
  16. whpalmer4
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    Okay, this is a little trickier, but not much :-) Area = length * width for a rectangle. If we double both length and width, what happens to area? New area = (2*old length)*(2*old width)

    • one year ago
  17. whpalmer4
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    Think of it like: you have a piece of notebook paper that covers the original area exactly. Now you want to make a model that has each side twice as long. Could you do that by putting down more paper? How much?

    • one year ago
  18. missashleyn
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    So would it become 4 times the original area?

    • one year ago
  19. whpalmer4
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    Yes! For the earlier problem, a similar mental model would be that the perimeter is a piece of string that goes around the roof. If you make each side 5x as long, you need 5x as much string to cover each side.

    • one year ago
  20. missashleyn
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    Why would it become 4 times the original area though?

    • one year ago
  21. whpalmer4
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    Because the area is length * width, and we doubled each one, so there's 2 * 2 = 4. Think of the paper model: if you had one sheet of notebook paper that fit the area exactly, then putting down 3 more sheets in the same orientation would make a rectangle that was twice the length and twice the width, right? And you'd have 4 * the area...

    • one year ago
  22. missashleyn
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    But if there's only one of something, you'd only need to add one more of the same thing to be twice the length.. right? I'm so confused! :(

    • one year ago
  23. whpalmer4
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    Basically, the idea is that you put the ratio you've changed the fundamental measurement by into the formula for the area, or perimeter, or volume, or shoe size, or whatever, and that gives you the ratio of the new to the old. Area = length * width, so when we put 2x length and 2x the width, we get 4x the area. Yes, only one more sheet of paper, but in each direction - both length and width.

    • one year ago
  24. whpalmer4
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    • one year ago
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  25. whpalmer4
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    Similarly, if we made each side be half the length they are now, we would up with (1/2)(1/2) = 1/4 the area.

    • one year ago
  26. missashleyn
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    Oh okay! Thank you very much :)

    • one year ago
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