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Solving a scale drawing word problem

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

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  • blobby green style avatar for user NaimaR
    is it just me im having a very hard time with these types of probs
    (12 votes)
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  • starky seedling style avatar for user lanejohnh
    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.
    (6 votes)
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  • winston baby style avatar for user NumberFanatic
    Sal uses too much vocab! What are dimensions! SAL IS TOO SMART! IM NOT!
    (2 votes)
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  • blobby green style avatar for user SCSTEELE04
    If an object 1'-6" long drawn at a scale of 1 1/2" = 1'-0", how long is the drawing?
    (6 votes)
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    • winston baby style avatar for user Alexander Pinto
      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)
  • duskpin seedling style avatar for user Abby
    Is there any way to do this without doing all the scratchpad work?
    (3 votes)
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    • blobby green style avatar for user Abhirami  Raghavan
      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)
  • winston baby style avatar for user CAPTAIN MAN AND KID DANGER
    How do I determine the scale factors for the three rectangles
    (4 votes)
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  • blobby green style avatar for user Harshil patel
    why you multiply directly 3 inches * 40
    (2 votes)
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    • female robot grace style avatar for user hannah
      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)
  • blobby green style avatar for user SLANDERMAN
    This is just an observation, I mean no disrespect to Sal, but at his explanation was a little hard to comprehend. i understood it but it took me a sec.
    (3 votes)
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  • hopper cool style avatar for user sstn
    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)
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  • aqualine ultimate style avatar for user Starby Cat
    Couldn't Sal just have done 3 x 1600, then divided by 12?
    (3 votes)
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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.