Question

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Directions: Type the correct answer in each box. Use numerals and/or variables instead of words. If necessary, use * for the multiplication symbol and / for division.

Hannah is having a new house built. The following is an initial blueprint of her new living room and entryway.

The perimeter of the scale drawing is centimeters.

If the scale is 1 centimeter = 5 feet, the perimeter of Hannah's actual living room and entryway would be feet.

Numerically, the value of the actual perimeter of Hannah's living room and entryway would be times the value of the perimeter of the scale drawing.

Based on these results, if the scale is 1 centimeter = k feet, the perimeter of Hannah's actual living room and entryway would be feet.
Picture: https://s3.amazonaws.com/platocdn/EdAssets/2706a5686a944c5f8a0401a50ce13b3c?ts=635138215229730000

Answer 1

@TheSmartOne

Answer 2

hint:
perimeter of the living room = 2*(5+4)= 2*9= 18 cm
perimeter of the entryway = 2*(2+1)= 2*3= 6 cm

Answer 3

@Michele_Laino

Answer 4

if we have: 1 cm = k feet, then we can write:
perimeter of the living room = 2*(5+4)= 2*9= 18 cm = 18*k feet
and:
perimeter of the entryway = 2*(2+1)= 2*3= 6 cm = 6*k feet

Answer 5

So that would be 24 right?

Answer 6

Ok so that answers the first part.

Answer 7

please wait...

the total perimeter is not equal to the sum of the single perimeters

Answer 8

Oh ok

Answer 9

total perimeter is:
4+5+6+1+2+4= 22 cm or 22*k feet

Answer 10

Wait... So you add them all together?

Answer 11

yes! I have applied the definition of perimeter

Answer 12

Awesome! So the first answer is 22 right?

Answer 13

yes! total perimeter, namely perimeter of Living Room + perimeter of entryway, is
22 cm

Answer 14

Ok so let's find the second one then.

Answer 15

Oh yea here is your Medal for helping me.

Answer 16

I would think that 5*22 would be that answer

Answer 17

yes! the perimeter of Living Room + entryway is 5*22 feet

Answer 18

YAY! Ok so that would be 110

Answer 19

ok!

Answer 20

Awesome and the next one...

Answer 21

it is simple, since we have 1 cm = k feet, so the perimeter is:
22*k feet

Answer 22

So the 3rd on is 22 as well?

Answer 23

ok!

Answer 24

Ok and the next one is...

Answer 25

we have to keep in mind that the actual perimeter is 5 times the perimeter of the scale drawing

Answer 26

the next answer is:
perimeter= 22* k feet
and
the actual perimeter is k times the scale drawing perimeter

Answer 27

Right so we would have to figure out what k meant. Right?

Answer 28

yes!

Answer 29

Ok so how do we find that out?

Answer 30

Are you still there @Michele_Laino

Answer 31

generally the value of k is chosen by the draughtsman

Answer 32

Who is that?

Answer 33

sorry my computer is blocking itself continuously

Answer 34

Oh it's ok so who is that?

Answer 35

k is called the scale ratio or the scale factor

Answer 36

So how do you figure it out?

Answer 37

Are you there @Michele_Laino

Answer 38

Ok but we don't know what K is.

Answer 39

Sorry my browser is blocking continuously, I try to exit from the site and then to enter into the site

Answer 40

Ok

Answer 41

please wait

Answer 42

Ok

Answer 43

Yay! Your back!

Answer 44

you can know the value of k from the text of your problem

Answer 45

as I promised!

Answer 46

So where is the information at in the question?

Answer 47

in this problem the value of k is generic, nevertheless we have to keep in mind that k is a number Greater than 1

Answer 48

Ok so would it be the 5?

Answer 49

in the first case it was 5,
in the second case it is generic, for example it can be 8, 20 and so on

Answer 50

So how would we know? Is it some random number?

Answer 51

no, it is not a random number. For example think about the perimeter of your Living Room, and divide it by 22 cm, wht you get is a possible value of k for example

Answer 52

Oh ok so that would be 1.2222222

Answer 53

I think it is a small number. Please what is the perimeter of your Living Room approximately, and measured in feet?

Answer 54

And if it was for the Entry it would be 3.66666666

Answer 55

for example the perimeter of my room is 16 meters or 1600 cm, so:
1600/22 = 72.7, then a possible value of k is 72.7 or about 73

Answer 56

Oh I think I got it! 22k

Answer 57

yes!

Answer 58

YAY!!!!! Ok I have more questions can you answer them for me?

Answer 59

ok!

Answer 60

I will open it in a new post and will tag you.

Answer 61

ok!