## missashleyn 2 years ago 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.

1. TajanaeXD

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

2. missashleyn

They didn't give me a perimeter :/

3. whpalmer4

We don't need to know the original perimeter.

4. missashleyn

Oh then I have absolutely no idea how to figure this out :(

5. TajanaeXD

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

6. whpalmer4

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?

7. missashleyn

I am so confused, ratio of what?

8. whpalmer4

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.

9. whpalmer4

The ratio of the new perimeter (bigger roof, with sides 5x as long) to the old perimeter (original roof).

10. missashleyn

So the perimeter will be 5 times the original perimeter?

11. whpalmer4

Yes!

12. TajanaeXD

Yep pretty much

13. missashleyn

Oh wow, that's confusing. I have another question like this.. could you help me with it too?

14. whpalmer4

Fire away, let's make it less confusing :-)

15. missashleyn

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.

16. whpalmer4

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)

17. whpalmer4

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?

18. missashleyn

So would it become 4 times the original area?

19. whpalmer4

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.

20. missashleyn

Why would it become 4 times the original area though?

21. whpalmer4

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...

22. missashleyn

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! :(

23. whpalmer4

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.

24. whpalmer4

25. whpalmer4

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.

26. missashleyn

Oh okay! Thank you very much :)