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Making a scale drawing

An urban planner needs your help in creating a scale drawing. Let's use our knowledge about scale factor, length, and area to assist. Created by Sal Khan.

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Video transcript

Cole is an urban planner. He wants to create a small scale drawing of a city block. The block is a square with an area of 8,100 square meters. Create a scale drawing of the block using a scale factor of 0.1. So the first thing we could think about, they give us the area of the block. And it's a square block. So it has the same length and width. So we could use that information to figure out the length and width of that block. So if it's a square, so let's imagine a square block right over here. And that this is, I guess we could call that the length. And then this is also going to be the length. It's going to be the same dimensions. We know that the area is just going to be the length times the length is going to be equal to 8,100. Or we could say that our length squared is going to be equal to 8,100. So what times itself is equal to 8,100? Well, the 81 might jump out at you. We know that 9 times 9 is equal to 81. But then we have these two zeroes right over here. But if we give each of these nines a zero, then we'll end up with two zeros in the product. So 90 times 90 is equal to 8,100. So now we know the dimensions of this square block. It's a 90 meter by 90 meter square block. It's my best attempt to draw a square block. Now that's the actual square block. Here let me draw it a little bit more like a square. My first drawing looked a little bit too much like a rhombus. So here you go. A little bit better attempt at a square. Now we want to create at a scale drawing of the block using a scale factor of 0.1. So the actual block, once again, is 90 meters by 90 meters. But in our scale drawing, and I'll do this in this purple color, we essentially want each of the dimensions to be 1/10 of their original dimensions. So we could take the scale factor and multiply it by each of these dimensions right over here. So 90 times 0.1, well that's just going to be 9. This right over here is a 1/10. A 1/10 of 90 meters is going to be 9 meters. And so this, when we draw the scale drawing at the scale that Cole intends to draw it at, we would draw 9 meters by 9 meters. And so let's go to the actual tool and draw a 9 meter by 9 meter square, or a 9 by 9 square. We can assume that the units here are in terms of meters. So let's see. I could draw in that dimension. OK, a 9 there. Let me use my mouse instead of my pen tool. It'll be easier. And then let me make this 9, this side 9, and then I could make this side 9. And then we are all set. It's a square. We see we have four right angles. And now we can check our answer. And we got it right.