Question

What is the change in the perimeter of a rectangle with side length of 60 cm and width of 78 cm if it is dilated by a scale factor of 1/6? 1/12??

Answer 1

(60*2+78*2)/(60*2*(1/6)+(1/6)*78*2) right?

Answer 2

whao i didnt do that much

Answer 3

is eithe 6 or 1/6:)

Answer 4

Trust yourselv @suzy4321 you probably did it right then :)

Answer 5

im not sure thanks Timo !

Answer 6

If I'm understanding the question correctly, "dilating by a factor of 1/6" means increasing the length/width by 1/6 its value. If all sides increase by a factor of 1/6 (so the new length/width is 7/6 the old length/width), the perimeter has also increased by a factor of 7/6.

Showing how this works mathematically is pretty straightforward. To figure out the answer, compare the perimeter before and after. It actually doesn't matter what they are, only what the scale factor is, so I'll call length "L" and width "W".

Starting perimeter: Po = 2L + 2W

If you increase a side by 1/6 its value, the new value is 7/6 the original. Thus the length becomes (7/6)L and the width becomes (7/6)W.

New perimeter: P = 2(7/6)L + 2(7/6)W

To compare the two perimeters, divide the two equations:

Po = 2L + 2W
---------------------
P = 2(7/6)L + 2(7/6)W

You can see that factoring out the 7/6 lets you reduce out 2L + 2W, leaving:

Po/P = 1/(7/6) --> P = (7/6)Po

Same thing goes for "dilating by 1/12" - the new perimeter is 13/12 times the starting one. You can sub in the numbers given in the question to prove to yourself this works.

Answer 7

1/6(60 cm + 60 cm + 78 cm + 78 cm)
1/6(276 cm)
46

Answer 8

i think it is 1/6 :) but that is just me.

Answer 9

thats if i understood correctly

Answer 10

yeah i believe so too
Matt was your estimation 1/6 as well or were you just teaaching me how to solve?

Answer 11

interestingly enought the 1/6 factor is your 1/6 factor. I suspected that.


THe formula is very linear :)

Answer 12

yeah i just dont reall y understand this that well

Answer 13

well just take formula and divide it by the formula adjusted for the new factor.

Answer 14

Well I was showing you how it worked...if you need an actual number for the change in perimeter, just find the difference between the new and old ones. For "dilating by 1/6," the starting perimeter is 2(60) + 2(78) = 276. From my explanation above, you know the new perimeter is 7/6 the old one, and 7/6*276 = 322. The new perimeter is 322 - 276 = 46 cm greater than the old one.

Note that this number, the difference, does depend on the actual length and width, unlike the scale factor.

Answer 15

ok Matt thanks for explaining that well your probably gonna turn into a mentor/champion here

Answer 16

Haha no problem happy to help