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## 7th grade (Eureka Math/EngageNY)

### Course: 7th grade (Eureka Math/EngageNY) > Unit 1

Lesson 4: Topic D: Ratios of scale drawings- Exploring scale copies
- Explore scale copies
- Corresponding points and sides of scaled shapes
- Corresponding sides and points
- Identifying scale copies
- Identify scale copies
- Identifying scale factors
- Identify scale factor in scale drawings
- Identifying values in scale copies
- Scale drawing: centimeters to kilometers
- Making a scale drawing
- Construct scale drawings
- Interpreting a scale drawing
- Solving a scale drawing word problem
- Scale drawing word problems

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# Solving a scale drawing word problem

CCSS.Math:

See how we solve a word problem by using a scale drawing and finding the scale factor. Created by Sal Khan.

## Want to join the conversation?

- at3:47, he says the dimensions is 40x40, presuming it's a square, but it says rectangular up above. I know a square is a rectangle, but how could he be sure those were the dimensions?(21 votes)
- He could do the reverse operation to check his work(10 votes)

- is it just me im having a very hard time with these types of probs(13 votes)
- He never says what would happen if you were trying to do an odd number!

It woud be a little bit ore complacated but he should at least talk about it.(7 votes) - Sal uses too much vocab! What are dimensions! SAL IS TOO SMART! IM NOT!(2 votes)
- Dimension is the length,width,height,or depth of something.(7 votes)

- If an object 1'-6" long drawn at a scale of 1 1/2" = 1'-0", how long is the drawing?(6 votes)
- If you dont understand what he is saying so basically he is trying to tell you how to get the area by multiplying with inches or anything to get the answer of the area for something a bit simple and better for you for those people who dont understand here is an example My area is 1800 to get it its 90 times 90 I got this by 9*9=18 and 90*90=1800 so he is trying to show you what he is doing and explaining the steps to do this type of method.(0 votes)

- Is there any way to do this without doing all the scratchpad work?(3 votes)
- It is all right to work with a pencil and paper but if you have the brain power, it is quite easy to do it in your brain. just find out the square root as shown in the video and work from there. It is always perfectly fine to use a pencil and paper and it is necesary alot of the time but on easier problems all you would need to do is jot down a few numbers!(4 votes)

**How do I determine the scale factors for the three rectangles**(4 votes)- You need to figure our how much each area is multiplied and that would be the scale factor, I think. Hope this helps!(1 vote)

- why you multiply directly 3 inches * 40(2 votes)
- Hey Harshil! So the information we have been given is that the real dining room is 1600 times larger in area. That means one side or one length of the dining room is 40 times larger (as explained by Sal).

I think the key word here is: "larger than". If the drawing is 3 inches, the real things is 40 times larger than that. So if we want to know how long the real dining room is, we can multiply these two numbers with each other.

Does that help?(4 votes)

- This is just an observation, I mean no disrespect to Sal, but at2:55his explanation was a little hard to comprehend. i understood it but it took me a sec.(3 votes)
- Correct me if I'm wrong, but shouldn't this question mention the fact that the dining room and blue print are both squares, or at least specify what type of rectangle they are? Does this mean that the length of one side of the dining room could vary?(1 vote)
- Because the question was only asking about the length of the dining room and not the width, it did not matter what the width was.(1 vote)

## Video transcript

Sally is an
architect who creates a blueprint of a
rectangular dining room. The area of the
actual dining room is 1,600 times
larger than the area of the dining room
on the blueprint. The length of the dining room
on the blueprint is 3 inches. What is the length of the
actual dining room in feet? So there's a couple of really
interesting things going on here. They give us the dimensions
of the blueprint in inches. We want the actual
length in feet. And then they tell us that the
area of the actual dining room is 1,600 times larger. So they're not saying that
the scale of the blueprint is at 1/1600. It's going to be
something less than that, and let's think about what
that scale is going to be. Let's just think about
some different scales. Let's say that this
is my blueprint, and this is the actual
reality of the dining room that we're thinking about. And my blueprint
is let's just say 1 by 1, just for the
sake of argument. Now, if this was a 1 by 1 square
and we increased the dimensions by a factor of 2, so
it's a 2 by 2 square, what's the area going to be? Well, this area
is going to be 4. This area is 1, this area is 4. So you notice that if we
increase by a factor of 2, it increase our area
by a factor of 4. Or another way of saying, if we
increase each of our dimensions by a factor of 2,
we're going to increase our area by a factor of 4. If instead we increased
each of our dimensions by a factor of 3, this
would be a 3 by 3 square, and we would increase our
area by a factor of 9. So notice, whatever factor
we're increasing the area by, it's going to be the
factor that we're increasing the
dimensions by squared. So let's just think
about it that way. So they're telling us
that we're increasing the area by 1,600 times. Actually, let me just clean
this thing up a little bit. So one way we could imagine
it, if our drawing did have an area of 1,
which we can't assume, but we could for the
sake of just figuring out what the scale of
the drawing is. Let me clear all of this here. So the area of the actual dining
room is 1,600 times larger, and so if the drawing
had an area of 1, then the area of the
actual dining room would be 1,600 So
what would I have to multiply each of
the dimensions by to get an area factor of 1,600? Well, if I multiply
this dimension by 40 and this dimension by 40,
we see 40 times 40 is 1,600. You might say, hey, Sal,
how did you figure out 40? Well, the 16 is a big clue. We know that 4 times
4 is equal to 16, and so if you gave a 0 to each
of these 4's, if you made it 40 times 40, then that
is going to be 1,600. So this information
right over here tells us that the scale
factor of the lengths is 40. That would result in an scale
factor for the area of 1,600. So that's a good starting point. Now let's go to the actual
dining room on the blueprint. So the actual dining
room on the blueprint doesn't have these dimensions. We just used that to figure
out the scaling factor. The actual dining
room on the blueprint has a length of 3 inches. So maybe it looks
something like this. They don't give us any
of the other dimensions, so we can even imagine a 3 inch
by 2 inch, 1 inch, whatever we want. We could even imagine a
3 inch by 3 inch square. They only care about the length. Now let's multiply both of
these by a factor of 40. And we only care
about the length here. They actually say what's the
length of the actual dining room. So let's multiply it,
and obviously, this is not drawn to scale. Let's multiply this
times a factor of 40. So 3 times 40 is 120,
and this, of course, is what we're referring
to as the length. Now, you might be tempted
to say OK, we're done. This will be 120. But remember, this
is 120 inches. So what is 120 inches
in terms of feet? Well, 1 foot is
equal to 12 inches. If we were to multiply
both of these times 10, we know that 10 feet
is equal to 120 inches. Or another way you could
have thought about it, you have 120 inches divided
by 12 inches per foot is going to give you 10. So 120 divided by-- 120 inches--
let me write it this way. 120 inches divided
by 12 inches per foot is going to give you 10 feet. So that's the actual length
of the dining room in feet.