Question

For the pair of similar figures, give (a) the ratio of the perimeters and (b) the ratio of the areas of the first figure to the second one.
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@michele_Laino

Answer 1

@amistre64

Answer 2

how do you think we should assess this?

Answer 3

i know perimeter would be4/3 but idk about the area

Answer 4

16 to 12 is not getting bigger

16(4/3) is not 12

Answer 5

16 to 16k for some scalar k gives us a 1:k ratio

Answer 6

wait so the first one isnt 4/3

Answer 7

of course not ....

now assume its a rectangle, what does the scalar do for the area of a rectangle?

Answer 8

im assuming A is to the left?

Answer 9

nothing

Answer 10

left to right

16 to 12

1: 12/16

wait, 4:3 might be accurate, but its more of a 1 : 3/4 ratio

Answer 11

what does your course notation suggest?

Answer 12

what do you mena

Answer 13

i mean, you are taking a course so you should be more closer to what the format needs to be then someone like me who is decades from when they took a class on this stuff.

Answer 14

o well i thought that the first answer is 4/3 but i dont know if that ratio changes for area

Answer 15

perimeter:

16+a+b+c scales by k to get a perimeter of 12+ak + bk + ck

for a ratio of

(16+a+b+c) : (12+ak + bk + ck)

(16+a+b+c) : k (16+ak + bk + ck)

1 : k ; and in this case 16k = 12, so k = 3/4

the perimeter is in a 1 : .75 ratio or however your course wishes you to format it

Answer 16

now its simpler to use a rectangle for showing how the scalar affects area

assume a rectangle of are 16a scales to a rectangle of (16k * ak)

16a : k^2 16a

1 : k^2 is the ratio of areas

Answer 17

regardless of the shape, the ratio of areas will be 1:k^2

Answer 18

so it doesnt change in ration?

Answer 19

1:k for linear measures like perimeter

1:k^2 for quadratic measures like area

1:k^3 for cubic measures like volume

there might be a pattern here.

Answer 20

no it goes to 16/9

Answer 21

yes

Answer 22

ok so 4/3 then 16/9

Answer 23

if thats the format your course wants, sure ... the number at least are valid :)